Semi-compatible and reciprocally continuous maps in weak non-Archimedean Menger PM-spaces

In this paper, we introduce semi-compatible maps and reciprocally continuous maps in weak non-Archimedean PM-spaces and establish a common fixed point theorem for such maps. Moreover, we show that, in the context of reciprocal continuity, the notions of compatibility and semi-compatibility of maps become equivalent. Our result generalizes several fixed point theorems in the sense that all maps involved in the theorem can be discontinuous even at the common fixed point.

On Ekeland's variational principle in partial metric spaces

In this paper, lower semi-continuous functions are used to extend Ekeland's variational principle to the class of parti al metric spaces. As consequences of our results, we obtain some fixed p oint theorems of Caristi and Clarke types.

Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation

Abstract We establish some fixed point theorems by introducing two new classes of contractive mappings in Menger PM-spaces. First, we prove our results for an α - ψ -type contractive mapping and then for a generalized β -type contractive mapping. Some examples and an application to Volterra type integral equation are given to support the obtained results.

A note on homoclinic solutions of (p,q)-Laplacian difference equations

We prove the existence of at least two positive homoclinic solutions for a discrete boundary value problem of equations driven by the (p,q) -Laplace operator. The properties of the nonlinearity ensure that the energy functional, corresponding to the problem, satisfies a mountain pass geometry and a Palais–Smale compactness condition.

The prognostic value of the myeloid-mediated immunosuppression marker Arginase-1 in classic Hodgkin lymphoma

// Alessandra Romano 1 , Nunziatina Laura Parrinello 1 , Calogero Vetro 1 , Daniele Tibullo 1 , Cesarina Giallongo 1 , Piera La Cava 1 , Annalisa Chiarenza 1 , Giovanna Motta 1 , Anastasia L. Caruso 1 , Loredana Villari 2 , Claudio Tripodo 3 , Sebastiano Cosentino 4 , Massimo Ippolito 4 , Ugo Consoli 5 , Andrea Gallamini 6 , Stefano Pileri 7 , Francesco Di Raimondo 1 1 Division of Hematology, AOU “Policlinico - Vittorio Emanuele”, University of Catania, Catania, Italy 2 Division of Pathology, AOU “Policlinico - Vittorio Emanuele”, Catania, Italy 3 Tumor Immunology Unit, Department of Health Science, University of Palermo, Palermo, Italy 4 Nuclear Medicine Center, Azienda Ospedaliera Cannizz…

Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations

We consider a nonlinear Dirichlet equation driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation). The hypotheses on the reaction f(z, x) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four nontrivial smooth solutions, respectively, all with sign information. We apply our multiplicity results to the particular case of a class of parametric (p, 2)-equations.

Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems

In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we …

Fixed point, attractors and weak fuzzy contractive mappings in a fuzzy metric space

Common Fixed points for multivalued generalized contractions on partial metric spaces

We establish some common fixed point results for multivalued mappings satisfying generalized contractive conditions on a complete partial metric space. The presented theorems extend some known results to partial metric spaces. We motivate our results by some given examples and an application for finding the solution of a functional equation arising in dynamic programming.

Common fixed point theorems for (ϕ, ψ)-weak contractions in fuzzy metric spaces

Motivated by Rhoades (Nonlinear Anal., 47 (2001), 2683--2693), on the lines of Khan et al. (Bull. Aust. Math. Soc., 30 (1984), 1-9) employing the idea of altering distances, we extend the notion of (ϕ, ψ)-weak contraction to fuzzy metric spaces and utilize the same to prove common fixed point theorems for four mappings in fuzzy metric spaces.

Multi-valued $$F$$ F -contractions in 0-complete partial metric spaces with application to Volterra type integral equation

We study the existence of fixed points for multi-valued mappings that satisfy certain generalized contractive conditions in the setting of 0-complete partial metric spaces. We apply our results to the solution of a Volterra type integral equation in ordered 0-complete partial metric spaces.

A blow-up result for a nonlinear wave equation on manifolds: the critical case

We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.

On an idea of Bakhtin and Czerwik for solving a first-order periodic problem

We study the existence of solutions to a first-order periodic problem involving ordinary differential equations, by using the quasimetric structure suggested by Bakhtin and Czerwik. The presented approach involves technical conditions and fixed point iterative schemes to yield new theoretical results guaranteeing the existence of at least one solution.

Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

Fixed point theorems for multivalued maps via new auxiliary function

We introduce a contractive condition involving new auxiliary function and prove a fixed point theorem for closed multivalued maps on complete metric spaces. An example and an application to integral equation are given in support of our findings.

A fixed point theorem for G-monotone multivalued mapping with application to nonlinear integral equations

We extend notion and theorem of [21] to the case of a multivalued mapping defined on a metric space endowed with a finite number of graphs. We also construct an example to show the generality of our result over existing results. Finally, we give an application to nonlinear integral equations

Some fixed point theorems for occasionally weakly compatible mappings in probabilistic semi-metric spaces

We prove some common fixed point theorems in probabilistic semi-metric spaces for occasionally weakly compatible mappings satisfying a generalized contractive condition. We give also results of common fixed point for mappings satisfying a condition of integral type.

Landesman-Lazer type (p, q)-equations with Neumann condition

We consider a Neumann problem driven by the (p, q)-Laplacian under the Landesman-Lazer type condition. Using the classical saddle point theorem and other classical results of the calculus of variations, we show that the problem has at least one nontrivial weak solution.

First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities

AbstractWe study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation $$\begin{aligned} iu_t+\Delta u=\lambda |u|^p+\mu |\nabla u|^q+w(x),\quad t>0,\, x\in {\mathbb {R}}^N, \end{aligned}$$ i u t + Δ u = λ | u | p + μ | ∇ u | q + w ( x ) , t > 0 , x ∈ R N , where $$N\ge 1$$ N ≥ 1 , $$p,q>1$$ p , q > 1 , $$\lambda ,\mu \in {\mathbb {C}}$$ λ , μ ∈ C , $$\lambda \ne 0$$ λ ≠ 0 , and $$u(0,\cdot ), w\in L^1_{\mathrm{loc}}({\mathbb {R}}^N,{\mathbb {C}})$$ u ( 0 , · ) , w ∈ L loc 1 ( R N , C ) . We consider both the cases where $$\mu =0$$ μ = 0 and $$\mu \ne 0$$ μ ≠ 0 , respectively. We establish existence/nonexistence of global weak solutions. In ea…

Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation

Abstract In this paper, we introduce new concepts of α-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from α-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.

Remarks on G-Metric Spaces

In 2005, Mustafa and Sims (2006) introduced and studied a new class of generalized metric spaces, which are called G-metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric) G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.

Best proximity point theorems for proximal cyclic contractions

The purpose of this article is to compute a global minimizer of the function $$x\longrightarrow d(x, Tx)$$ , where T is a proximal cyclic contraction in the framework of a best proximally complete space, thereby ensuring the existence of an optimal approximate solution, called a best proximity point, to the equation $$Tx=x$$ when T is not necessarily a self-mapping.

A common fixed point theorem for two weakly compatible pairs in G-metric spaces using the property E.A

In view of the fact that the fixed point theory provides an efficient tool in many fields of pure and applied sciences, we use the notion of the property E.A to prove a common fixed point theorem for weakly compatible mappings. The presented results are applied to obtain the solution of an integral equation and the bounded solution of a functional equation arising in dynamic programming.

Impact of common property (E.A.) on fixed point theorems in fuzzy metric spaces

We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.

Nonlinear Robin problems with unilateral constraints and dependence on the gradient

We consider a nonlinear Robin problem driven by the p-Laplacian, with unilateral constraints and a reaction term depending also on the gradient (convection term). Using a topological approach based on fixed point theory (the Leray-Schauder alternative principle) and approximating the original problem using the Moreau-Yosida approximations of the subdifferential term, we prove the existence of a smooth solution.

Intravenous injection of bortezomib, melphalan and dexamethasone in refractory and relapsed multiple myeloma

Abstract Background A combination of bortezomib (1.3 mg/m2), melphalan (5 mg/m2), and dexamethasone (40 mg) (BMD), with all three drugs given as a contemporary intravenous administration, was retrospectively evaluated. Patients and methods Fifty previously treated (median 2 previous lines) patients with myeloma (33 relapsed and 17 refractory) were assessed. The first 19 patients were treated with a twice-a-week (days 1, 4, 8, 11, ‘base’ schedule) administration while, in the remaining 31 patients, the three drugs were administered once a week (days 1, 8, 15, 22, ‘weekly’ schedule). Results Side-effects were predictable and manageable, with prominent haematological toxicity, and a better tox…

On the critical behavior for time-fractional pseudo-parabolic type equations with combined nonlinearities

AbstractWe are concerned with the existence and nonexistence of global weak solutions for a certain class of time-fractional inhomogeneous pseudo-parabolic-type equations involving a nonlinearity of the form $|u|^{p}+\iota |\nabla u|^{q}$ | u | p + ι | ∇ u | q , where $p,q>1$ p , q > 1 , and $\iota \geq 0$ ι ≥ 0 is a constant. The cases $\iota =0$ ι = 0 and $\iota >0$ ι > 0 are discussed separately. For each case, the critical exponent in the Fujita sense is obtained. We point out two interesting phenomena. First, the obtained critical exponents are independent of the fractional orders of the time derivative. Secondly, in the case $\iota >0$ ι > 0 , we show that the gradie…

Superlinear Robin Problems with Indefinite Linear Part

We consider a semilinear Robin problem with an indefinite linear part and a superlinear reaction term, which does not satisfy the usual in such cases AR condition. Using variational methods, together with truncation–perturbation techniques and Morse theory (critical groups), we establish the existence of three nontrivial solutions. Our result extends in different ways the multiplicity theorem of Wang.

Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method

For the homogeneous Dirichlet problem involving a system of equations driven by \begin{document}$(p,q)$\end{document} -Laplacian operators and general gradient dependence we prove the existence of solutions in the ordered rectangle determined by a subsolution-supersolution. This extends the preceding results based on the method of subsolution-supersolution for systems of elliptic equations. Positive and negative solutions are obtained.

Metabolic parameters and adipokine profile during GH replacement therapy in children with GH deficiency

Objective: GH replacement therapy in children with GH deficiency (GHD) mainly promotes linear growth. Not only have very few studies fully analyzed the metabolic consequences of GH therapy, but also the question as to whether GH may affect adipokine secretion has been insufficiently investigated. Our aim was to study the effects of GH replacement therapy on auxological data, lipid and glycemic profiles, insulin homeostasis (HOMA-IR) and serum adipokines in children. Methods: This was a 1-year prospective study. Thirty-four GHD children (11.6 ± 2.6 years) and thirty healthy matched controls were enrolled. Children affected by GHD were studied both before beginning continuous GH replacement t…

Coupled common fixed point theorems in partially ordered G-metric spaces for nonlinear contractions

The aim of this paper is to prove coupled coincidence and coupled common fixed point theorems for a mixed $g$-monotone mapping satisfying nonlinear contractive conditions in the setting of partially ordered $G$-metric spaces. Present theorems are true generalizations of the recent results of Choudhury and Maity [Math. Comput. Modelling 54 (2011), 73-79], and Luong and Thuan [Math. Comput. Modelling 55 (2012) 1601-1609].

Nonlinear concave-convex problems with indefinite weight

We consider a parametric nonlinear Robin problem driven by the p-Laplacian and with a reaction having the competing effects of two terms. One is a parametric (Formula presented.) -sublinear term (concave nonlinearity) and the other is a (Formula presented.) -superlinear term (convex nonlinearity). We assume that the weight of the concave term is indefinite (that is, sign-changing). Using the Nehari method, we show that for all small values of the parameter (Formula presented.), the problem has at least two positive solutions and also we provide information about their regularity.

An elliptic equation on n-dimensional manifolds

We consider an elliptic equation driven by a p-Laplacian-like operator, on an n-dimensional Riemannian manifold. The growth condition on the right-hand side of the equation depends on the geometry of the manifold. We produce a nontrivial solution by using a Palais–Smale compactness condition and a mountain pass geometry.

Approximate fixed points of set-valued mapping in b-metric space

We establish existence results related to approximate fixed point property of special types of set-valued contraction mappings, in the setting of b-metric spaces. As consequences of the main theorem, we give some fixed point results which generalize and extend various fixed point theorems in the existing literature. A simple example illustrates the new theory. Finally, we apply our results to establishing the existence of solution for some differential and integral problems.

Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces

Abstract In this paper, we establish two coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. The theorems presented extend some results due to Ciric (2009) [3] . An example is given to illustrate the usability of our results.

A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence

The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.

On Branciari’s theorem for weakly compatible mappings

AbstractIn a recent paper B. Samet and H. Yazidi [B. Samet, H. Yazidi, An extension of Banach fixed point theorem for mappings satisfying a contractive condition of integral type, Ital. J. Pure Appl. Math. (in press)] have obtained an interesting theorem for mappings satisfying a contractive condition of integral type. The aim of this note is to present a generalization of their main result.

On generalized weakly G-contraction mapping in G-metric spaces

AbstractIn this paper, we establish some common fixed point results for two self-mappings f and g on a generalized metric space X. To prove our results we assume that f is a generalized weakly G-contraction mapping of types A and B with respect to g.

A remark on differentiable functions with partial derivatives in Lp

AbstractWe consider a definition of p,δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p,δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.

From metric spaces to partial metric spaces

Motivated by experience from computer science, Matthews (1994) introduced a nonzero self-distance called a partial metric. He also extended the Banach contraction principle to the setting of partial metric spaces. In this paper, we show that fixed point theorems on partial metric spaces (including the Matthews fixed point theorem) can be deduced from fixed point theorems on metric spaces. New fixed point theorems on metric spaces are established and analogous results on partial metric spaces are deduced. MSC:47H10, 54H25.

Solutions with sign information for nonlinear Robin problems with no growth restriction on reaction

We consider a parametric nonlinear Robin problem driven by a nonhomogeneous differential operator. The reaction is a Carathéodory function which is only locally defined (that is, the hypotheses concern only its behaviour near zero). The conditions on the reaction are minimal. Using variational tools together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter λ > 0, the problem has at least three nontrivial smooth solutions, two of constant sign and the third nodal.

Fixed point theorems for twisted (α,β)-ψ-contractive type mappings and applications

The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.

Iterative Reconstruction of Signals on Graph

We propose an iterative algorithm to interpolate graph signals from only a partial set of samples. Our method is derived from the well known Papoulis-Gerchberg algorithm by considering the optimal value of a constant involved in the iteration step. Compared with existing graph signal reconstruction algorithms, the proposed method achieves similar or better performance both in terms of convergence rate and computational efficiency.

Set-valued mappings in partially ordered fuzzy metric spaces

Abstract In this paper, we provide coincidence point and fixed point theorems satisfying an implicit relation, which extends and generalizes the result of Gregori and Sapena, for set-valued mappings in complete partially ordered fuzzy metric spaces. Also we prove a fixed point theorem for set-valued mappings on complete partially ordered fuzzy metric spaces which generalizes results of Mihet and Tirado. MSC:54E40, 54E35, 54H25.

Multiple solutions with sign information for semilinear Neumann problems with convection

We consider a semilinear Neumann problem with convection. We assume that the drift coefficient is indefinite. Using the theory of nonlinear operators of monotone type, together with truncation and comparison techniques and flow invariance arguments, we prove a multiplicity theorem producing three nontrivial smooth solutions (positive, negative and nodal).

On multivalued weakly Picard operators in partial Hausdorff metric spaces

We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.

Common fixed points for discontinuous mappings in fuzzy metric spaces

In this paper we prove some common fixed point theorems for fuzzy contraction respect to a mapping, which satisfies a condition of weak compatibility. We deduce also fixed point results for fuzzy contractive mappings in the sense of Gregori and Sapena.

Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations

We establish a best proximity pair theorem for noncyclic φ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic φ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations.

Krasnosel'skiĭ-Schaefer type method in the existence problems

We consider a general integral equation satisfying algebraic conditions in a Banach space. Using Krasnosel'skii-Schaefer type method and technical assumptions, we prove an existence theorem producing a periodic solution of some nonlinear integral equation.

Fuzzy fixed points of generalized F2-geraghty type fuzzy mappings and complementary results

The aim of this paper is to introduce generalized F2-Geraghty type fuzzy mappings on a metric space for establishing the existence of fuzzy fixed points of such mappings. As an application of our result, we obtain the existence of common fuzzy fixed point for a generalized F2-Geraghty type fuzzy hybrid pair. These results unify, generalize and complement various known comparable results in the literature. An example and an application to theoretical computer science are presented to support the theory proved herein. Also, to suggest further research on fuzzy mappings, a Feng–Liu type theorem is proved.

Nonlinear multivalued Duffing systems

We consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is convex valued or not). Also, we show that the solutions of the nonconvex problem are dense in those of the convex (relaxation theorem). Our work extends the recent one by Kalita-Kowalski (JMAA, https://doi.org/10.1016/j.jmaa. 2018.01.067).

Optimization Problems via Best Proximity Point Analysis

1 Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia 2Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey 3 Department of Mathematics, Babes-Bolyai University, Kogalniceanu Street No. 1, 400084 Cluj-Napoca, Romania 4Universita Degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi 34, 90123 Palermo, Italy

Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator

We prove the existence of weak solutions to the Dirichlet boundary value problem for equations involving the $p(x)$-Laplacian-like operator in the principal part, with reaction term satisfying a sub-critical growth condition. We establish the existence of at least one nontrivial weak solution and three weak solutions, by using variational methods and critical point theory.

Pairs of nontrivial smooth solutions for nonlinear Neumann problems

Abstract We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator with a reaction term that exhibits strong resonance at infinity. Using variational tools based on the critical point theory, we prove the existence of two nontrivial smooth solutions.

Fixed point and homotopy results for mixed multi-valued mappings in 0-complete partial metric spaces*

We give sufficient conditions for the existence of common fixed points for a pair of mixed multi-valued mappings in the setting of 0-complete partial metric spaces. An example is given to demonstrate the usefulness of our results over the existing results in metric spaces. Finally, we prove a homotopy theorem via fixed point results.

Large Time Behavior for Inhomogeneous Damped Wave Equations with Nonlinear Memory

We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory ϕtt(t,&omega

Meir-Keeler Type Contractions for Tripled Fixed Points

Abstract In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.

Three solutions to mixed boundary value problem driven by p(z)-Laplace operator

We prove the existence of at least three weak solutions to a mixed Dirichlet–Neumann boundary value problem for equations driven by the p(z)-Laplace operator in the principal part. Our approach is variational and use three critical points theorems.

Multiple solutions for (p,2)-equations at resonance

We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian and a reaction term which is (p− 1)-linear near ±∞ and resonant with respect to any nonprincipal variational eigenvalue of (−∆p, W01,p(Ω)). Using variational tools together with truncation and comparison techniques and Morse Theory (critical groups), we establish the existence of six nontrivial smooth solutions. For five of them we provide sign information and order them.

A fixed point theorem for uniformly locally contractive mappings in a C-chainable cone rectangular metric space

Recently, Azam, Arshad and Beg [ Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math. 2009] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result.

A fixed-point problem with mixed-type contractive condition

We consider a fixed-point problem for mappings involving a mixed-type contractive condition in the setting of metric spaces. Precisely, we establish the existence and uniqueness of fixed point using the recent notions of $F$-contraction and $(H,\varphi)$-contraction.

(p,2)-equations resonant at any variational eigenvalue

We consider nonlinear elliptic Dirichlet problems driven by the sum of a p-Laplacian and a Laplacian (a (p,2) -equation). The reaction term at ±∞ is resonant with respect to any variational eigenvalue of the p-Laplacian. We prove two multiplicity theorems for such equations.

On the existence of bounded solutions to a class of nonlinear initial value problems with delay

We consider a class of nonlinear initial value problems with delay. Using an abstract fixed point theorem, we prove an existence result producing a unique bounded solution.

Recent Developments on Fixed Point Theory in Function Spaces and Applications to Control and Optimization Problems

1Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Raipur, Chhattisgarh 492101, India 2Department of Mathematics and AppliedMathematics, University of Pretoria, Private Bag X20, Hatfield, Pretoria 0028, South Africa 3Departement de Mathematiques et de Statistique, Universite de Montreal, CP 6128, Succursale Centre-Ville, Montreal, QC, Canada H3C 3J7 4Department of Mathematics and Informatics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy

Comments on the paper "COINCIDENCE THEOREMS FOR SOME MULTIVALUED MAPPINGS" by B. E. RHOADES, S. L. SINGH AND CHITRA KULSHRESTHA

The aim of this note is to point out an error in the proof of Theorem 1 in the paper entitled “Coincidence theorems for some multivalued mappings” by B. E. Rhoades, S. L. Singh and Chitra Kulshrestha [Internat. J. Math. & Math. Sci., 7 (1984), 429-434], and to indicate a way to repair it.

Positive solutions for parametric singular Dirichlet(p,q)-equations

Abstract We consider a nonlinear elliptic Dirichlet problem driven by the ( p , q ) -Laplacian and a reaction consisting of a parametric singular term plus a Caratheodory perturbation f ( z , x ) which is ( p − 1 ) -linear as x → + ∞ . First we prove a bifurcation-type theorem describing in an exact way the changes in the set of positive solutions as the parameter λ > 0 moves. Subsequently, we focus on the solution multifunction and prove its continuity properties. Finally we prove the existence of a smallest (minimal) solution u λ ∗ and investigate the monotonicity and continuity properties of the map λ → u λ ∗ .

Constant sign and nodal solutions for parametric anisotropic $(p, 2)$-equations

We consider an anisotropic ▫$(p, 2)$▫-equation, with a parametric and superlinear reaction term.Weshow that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups. Spletna objava: 9. 9. 2021. Abstract. Bibliografija: str. 1076.

JH-Operators and Occasionally Weakly g-Biased Pairs in Fuzzy Symmetric Spaces

We introduce the notions of $\mathcal{JH}$-operators and occasionally weakly $g$-biased mappings in fuzzy symmetric spaces to prove common fixed point theorems for self-mappings satisfying a generalized mixed contractive condition. We also prove analogous results for two pairs of $\mathcal{JH}$-operators by assuming symmetry only on the set of points of coincidence. These results unify, extend and complement many results existing in the recent literature. We give also an application of our results to product spaces.

Common fixed points for locally lipschitz mappings

Best Proximity Point Results in Non-Archimedean Fuzzy Metric Spaces

We consider the problem of finding a best proximity point which achieves the minimum distance between two nonempty sets in a non-Archimedean fuzzy metric space. First we prove the existence and uniqueness of the best proximity point by using di fferent contractive conditions, then we present some examples to support our best proximity point theorems.

Common Fixed Point Theorems for Weakly Compatible Maps Satisfying a General Contractive Condition

We introduce a new generalized contractive condition for four mappings in the framework of metric space. We give some common fixed point results for these mappings and we deduce a fixed point result for weakly compatible mappings satisfying a contractive condition of integral type.

Fixed-Point Theorems in Complete Gauge Spaces and Applications to Second-Order Nonlinear Initial-Value Problems

We establish fixed-point results for mappings and cyclic mappings satisfying a generalized contractive condition in a complete gauge space. Our theorems generalize and extend some fixed-point results in the literature. We apply our obtained results to the study of existence and uniqueness of solution to a second-order nonlinear initial-value problem.

A note on best approximation in 0-complete partial metric spaces

We study the existence and uniqueness of best proximity points in the setting of 0-complete partial metric spaces. We get our results by showing that the generalizations, which we have to consider, are obtained from the corresponding results in metric spaces. We introduce some new concepts and consider significant theorems to support this fact.

Coupled coincidence points for compatible mappings satisfying mixed monotone property

We establish coupled coincidence and coupled fixed point results for a pair of mappings satisfying a compatibility hypothesis in partially ordered metric spaces. An example is given to illustrate our obtained results.

Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction

We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.

Multiple nodal solutions for semilinear robin problems with indefinite linear part and concave terms

We consider a semilinear Robin problem driven by Laplacian plus an indefinite and unbounded potential. The reaction function contains a concave term and a perturbation of arbitrary growth. Using a variant of the symmetric mountain pass theorem, we show the existence of smooth nodal solutions which converge to zero in $C^1(\overline{\Omega})$. If the coefficient of the concave term is sign changing, then again we produce a sequence of smooth solutions converging to zero in $C^1(\overline{\Omega})$, but we cannot claim that they are nodal.

Absolute continuity for Banach space valued mappings

We consider the notion of p,λ,δ-absolute continuity for Banach space valued mappings introduced in [2] for real valued functions and for λ = 1. We investigate the validity of some basic properties that are shared by n, λ-absolutely continuous functions in the sense of Maly and Hencl. We introduce the class $δ-BV^p_{λ,loc}$ and we give a characterization of the functions belonging to this class.

Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations

In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.

The behavior of solutions of a parametric weighted (p, q)-laplacian equation

<abstract><p>We study the behavior of solutions for the parametric equation</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ -\Delta_{p}^{a_1} u(z)-\Delta_{q}^{a_2} u(z) = \lambda |u(z)|^{q-2} u(z)+f(z,u(z)) \quad \mbox{in } \Omega,\, \lambda >0, $\end{document} </tex-math></disp-formula></p> <p>under Dirichlet condition, where $ \Omega \subseteq \mathbb{R}^N $ is a bounded domain with a $ C^2 $-boundary $ \partial \Omega $, $ a_1, a_2 \in L^\infty(\Omega) $ with $ a_1(z), a_2(z) > 0 $ for a.a. $ z \in \Omega $, $ p, q \in (1, \infty) $ and $ \Delta_{p}^{a_1}, \Delta_{q}^{a_2} $ are weighted …

Best proximity point results for modified α-proximal C-contraction mappings

First we introduce new concepts of contraction mappings, then we establish certain best proximity point theorems for such kind of mappings in metric spaces. Finally, as consequences of these results, we deduce best proximity point theorems in metric spaces endowed with a graph and in partially ordered metric spaces. Moreover, we present an example and some fixed point results to illustrate the usability of the obtained theorems. MSC:46N40, 46T99, 47H10, 54H25.

Primitive rispetto all’ oscillazione

We study the real valued functions having a primitive with respect to the oscillation or a primitive with respect to the oscillation up to anegligible set.

Superlinear (p(z), q(z))-equations

AbstractWe consider Dirichlet boundary value problems for equations involving the (p(z), q(z))-Laplacian operator in the principal part and prove the existence of one and three nontrivial weak solutions, respectively. Here, the nonlinearity in the reaction term is allowed to depend on the solution, but does not satisfy the Ambrosetti–Rabinowitz condition. The hypotheses on the reaction term ensure that the Euler–Lagrange functional, associated to the problem, satisfies both the -condition and a mountain pass geometry.

Positive solutions for singular (p, 2)-equations

We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.

Fixed Point Theorems with Applications to the Solvability of Operator Equations and Inclusions on Function Spaces

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia 2Department of Mathematical Analysis, University of Valencia, Spain 3Centre Universitaire Polydisciplinaire, Kelaa des Sraghna, Morocco 4Universite Cadi Ayyad, Laboratoire de Mathematiques et de Dynamique de Populations, Marrakech, Morocco 5Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy

Adrenal morphology and function in acromegalic patients in relation to disease activity.

Visceromegaly is a common consequence of acromegaly. However, few studies investigated the chronic effects of growth hormone on adrenal glands. Our aim was to evaluate adrenal morphology and function in a cohort of acromegalic patients in relation to disease activity. Twenty-six acromegalics (10 males and 16 females) and 21 healthy subjects were investigated. Gland morphology was evaluated by computerized axial tomography, measuring central, lateral, and medial adrenal segments. Uncontrolled acromegalics showed increased volume of all adrenal segments, higher urinary free cortisol (UFC), and lower morning adrenocorticotropic hormone in comparison with healthy subjects. However, normal corti…

The Existence of Solutions for Local Dirichlet (r(u),s(u))-Problems

In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the spac…

Singular Neumann (p, q)-equations

We consider a nonlinear parametric Neumann problem driven by the sum of a p-Laplacian and of a q-Laplacian and exhibiting in the reaction the competing effects of a singular term and of a resonant term. Using variational methods together with suitable truncation and comparison techniques, we show that for small values of the parameter the problem has at least two positive smooth solutions.

Fixed points for weak alpha-psi-contractions in partial metric spaces

Recently, Samet et al. (2012) introduced the notion of $\alpha $ - $\psi $ -contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weak $\alpha $ - $\psi $ -contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and $$\pm \infty $$ . Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.

Nonexistence of global weak solutions for a nonlinear Schrodinger equation in an exterior domain

We study the large-time behavior of solutions to the nonlinear exterior problem L u ( t , x ) = &kappa

Positive solutions for singular double phase problems

Abstract We study the existence of positive solutions for a class of double phase Dirichlet equations which have the combined effects of a singular term and of a parametric superlinear term. The differential operator of the equation is the sum of a p-Laplacian and of a weighted q-Laplacian ( q p ) with discontinuous weight. Using the Nehari method, we show that for all small values of the parameter λ > 0 , the equation has at least two positive solutions.

MR3098564 Reviewed Al-Thagafi, M. A.; Shahzad, Naseer Krasnosel'skii-type fixed-point results. J. Nonlinear Convex Anal. 14 (2013), no. 3, 483–491. (Reviewer: Calogero Vetro) 47H10 (47H09)

The Krasnosel'skii fixed-point theorem is a powerful tool in dealing with various types of integro-differential equations. The initial motivation of this theorem is the fact that the inversion of a perturbed differential operator may yield the sum of a continuous compact mapping and a contraction mapping. Following and improving this idea, many fixed-point results were proved.\\ The authors present significant and interesting contributions in this direction. In particular, they give the following main theorem: \begin{theorem} Let $M$ be a nonempty bounded closed convex subset of a Banach space $E$, $S:M \to E$ and $T:M \to E$. Suppose that \begin{itemize} \item[(a)] $S$ is 1-set-contractive…

Best proximity point theorems for rational proximal contractions

Abstract We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results. MSC:41A65, 46B20, 47H10.

Solutions for parametric double phase Robin problems

We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p − 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 + .

GH-treatment improves growth and reduces the severity of fibrosis and hypertansaminasemia in a prepubertal child with sclerosant cholangiopathy

Best approximation and variational inequality problems involving a simulation function

We prove the existence of a g-best proximity point for a pair of mappings, by using suitable hypotheses on a metric space. Moreover, we establish some convergence results for a variational inequality problem, by using the variational characterization of metric projections in a real Hilbert space. Our results are applicable to classical problems of optimization theory.

WITHDRAWN: An efficient multiscale algorithm

The publisher regrets that this article has been temporarily removed. The reason for the overturn of the decision on ACHA-16-25 from Acceptance to Rejection is: One of the colleagues of the authors, Elisa Francomano, claims that the authors submitted the manuscript to ACHA without her knowledge and omitting her as one of the authors. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy .

From fuzzy metric spaces to modular metric spaces: a fixed point approach

We propose an intuitive theorem which uses some concepts of auxiliary functions for establishing existence and uniqueness of the fixed point of a self-mapping. First we work in the setting of fuzzy metric spaces in the sense of George and Veeramani, then we deduce some consequences in modular metric spaces. Finally, a sample homotopy result is derived making use of the main theorem.

Coupled fixed point, F-invariant set and fixed point of N-order

‎In this paper‎, ‎we establish some new coupled fixed point theorems in complete metric spaces‎, ‎using a new concept of $F$-invariant set‎. ‎We introduce the notion of fixed point of $N$-order as natural extension of that of coupled fixed point‎. ‎As applications‎, ‎we discuss and adapt the presented results to the setting of partially ordered cone metric spaces‎. ‎The presented results extend and complement some known existence results from the literature‎.

Multiple solutions for parametric double phase Dirichlet problems

We consider a parametric double phase Dirichlet problem. Using variational tools together with suitable truncation and comparison techniques, we show that for all parametric values [Formula: see text] the problem has at least three nontrivial solutions, two of which have constant sign. Also, we identify the critical parameter [Formula: see text] precisely in terms of the spectrum of the [Formula: see text]-Laplacian.

Homoclinic Solutions of Nonlinear Laplacian Difference Equations Without Ambrosetti-Rabinowitz Condition

The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.

Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces

Abstract In this paper, we introduce the concept of a partial Hausdorff metric. We initiate study of fixed point theory for multi-valued mappings on partial metric space using the partial Hausdorff metric and prove an analogous to the well-known Nadlerʼs fixed point theorem. Moreover, we give a homotopy result as application of our main result.

A coincidence-point problem of Perov type on rectangular cone metric spaces

We consider a coincidence-point problem in the setting of rectangular cone metric spaces. Using alpha-admissible mappings and following Perov's approach, we establish some existence and uniqueness results for two self-mappings. Under a compatibility assumption, we also solve a common fixed-point problem.

Common best proximity points and global optimal approximate solutions for new types of proximal contractions

Let $(\mathcal{X},d)$ be a metric space, $\mathcal{A}$ and $\mathcal{B}$ be two non-empty subsets of $\mathcal{X}$ and $\mathcal{S},\mathcal{T}: \mathcal{A} \to \mathcal{B}$ be two non-self mappings. In view of the fact that, given any point $x \in \mathcal{A}$, the distances between $x$ and $\mathcal{S}x$ and between $x$ and $\mathcal{T}x$ are at least $d(\mathcal{A}, \mathcal{B}),$ which is the absolute infimum of $d(x, \mathcal{S} x)$ and $d(x, \mathcal{T} x)$, a common best proximity point theorem affirms the global minimum of both the functions $x \to d(x, \mathcal{S}x)$ and $x \to d(x, \mathcal{T}x)$ by imposing the common approximate solution of the equations $\mathcal{S}x = x$ and $…

Iterative Methods for Signal Reconstruction on Graphs

In applications such as social, energy, transportation, sensor, and neuronal networks, big data naturally reside on the vertices of graphs. Each vertex stores a sample, and the collection of these samples is referred to as a graph signal. The product of the network graph with the time series graph is considered as underlying structure for the evolution through time of graph signal “snapshots”. The framework of signal processing on graphs [4] extends concepts and methodologies from classical discrete signal processing. The task of sampling and recovery is one of the most critical topics in the signal processing community. In this talk, we present some localized iterative methods, obtained by…

The effects of convolution and gradient dependence on a parametric Dirichlet problem

Our objective is to study a new type of Dirichlet boundary value problem consisting of a system of equations with parameters, where the reaction terms depend on both the solution and its gradient (i.e., they are convection terms) and incorporate the effects of convolutions. We present results on existence, uniqueness and dependence of solutions with respect to the parameters involving convolutions.

From Caristi’s Theorem to Ekeland’s Variational Principle in 0σ-Complete Metric-Like Spaces

We discuss the extension of some fundamental results in nonlinear analysis to the setting of 0σ-complete metric-like spaces. Then, we show that these extensions can be obtained via the corresponding results in standard metric spaces.

A Binary Particle Swarm Optimization Algorithm for a Double Auction Market

In this paper, we shall show the design of a multi-unit double auction (MDA) market. It should be enough robust, flexible and sufficiently efficient in facilitating exchanges. In a MDA market, sellers and buyers submit respectively asks and bids. A trade is made if a buyers bid exceeds a sellers ask. A sellers ask may match several buyers bids and a buyers bid may satisfy several sellers asks. The trading rule of a market defines the organization, information exchange process, trading procedure and clearance rules of the market. The mechanism is announced before the opening of the market so that every agent knows how the market will operate in advance. These autonomous agents pursue their o…

Three existence theorems for weak contractions of Matkowski type

We prove three generalizations of Matkowski’s fixed point theorems for weakly contractions.

MR3104897 Reviewed Mawhin, J. Variations on some finite-dimensional fixed-point theorems. Translation of Ukraïn. Mat. Zh. 65 (2013), no. 2, 266–272. Ukrainian Math. J. 65 (2013), no. 2, 294–301. (Reviewer: Calogero Vetro) 54H25 (47H10)

Inglese:The author presents an interesting discussion on three fundamental results in the literature and related theory: the Poincaré-Miranda theorem [C. Miranda, Boll. Un. Mat. Ital. (2) 3 (1940), 5–7; MR0004775 (3,60b)], the Pireddu-Zanolin fixed point theorem [M. Pireddu and F. Zanolin, Topol. Methods Nonlinear Anal. 30 (2007), no. 2, 279–319; MR2387829 (2009a:37032)] and the Zgliczyński fixed point theorem [P. Zgliczyński, Nonlinear Anal. 46 (2001), no. 7, Ser. A: Theory Methods, 1039–1062; MR1866738 (2002h:37032)]. The author provides generalizations of the last two fixed point theorems by using the original technique that he developed in a previous paper and the Poincaré-Miranda theor…

Nonlinear Nonhomogeneous Elliptic Problems

We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven…

Hybrid coincidence and common fixed point theorems in Menger probabilistic metric spaces under a strict contractive condition with an application

Abstract We prove some coincidence and common fixed point theorems for two hybrid pairs of mappings in Menger spaces satisfying a strict contractive condition. An illustrative example is given to support the genuineness of our extension besides deriving some related results. Then, we establish the corresponding common fixed point theorems in metric spaces. Finally, we utilize our main result to obtain the existence of a common solution for a system of Volterra type integral equations.

Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems

In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we …

Fixed points of weakly compatible mappings satisfying generalized $\varphi$-weak contractions

In this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a \(\varphi \)-weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature.

Incidence and Management Of Venous Thrombosis In Acute Leukemia: A Multicenter Study

Abstract Background Venous thrombosis (VT) frequently complicates the clinical course of cancer. Reported incidence of VT in many hematological neoplasms is up to 10%, a value comparable to that of solid tumors. Available data on the incidence and management of VT in Acute Leukemia (AL) are scanty and quite discordant. We have performed a multicenter retrospective study with the primary objective to evaluate the incidence of venous thrombotic complications in a population of patients with AL. Secondary objective was to evaluate the management of these complications in patients with AL. Materials and Methods Available clinical records of out and in-patients diagnosed with AL from January 200…

Parametric and nonparametric A-Laplace problems: Existence of solutions and asymptotic analysis

We give sufficient conditions for the existence of weak solutions to quasilinear elliptic Dirichlet problem driven by the A-Laplace operator in a bounded domain Ω. The techniques, based on a variant of the symmetric mountain pass theorem, exploit variational methods. We also provide information about the asymptotic behavior of the solutions as a suitable parameter goes to 0 + . In this case, we point out the existence of a blow-up phenomenon. The analysis developed in this paper extends and complements various qualitative and asymptotic properties for some cases described by homogeneous differential operators.

A fixed point theorem in G-metric spaces via alpha-series

In the context of G-metric spaces we prove a common fixed point theorem for a sequence of self mappings using a new concept of alpha-series.

Normalized Solutions to the Fractional Schrödinger Equation with Potential

AbstractThis paper is concerned with the existence of normalized solutions to a class of Schrödinger equations driven by a fractional operator with a parametric potential term. We obtain minimization of energy functional associated with that equations assuming basic conditions for the potential. Our work offers a partial extension of previous results to the non-local case.

AN ADDENDUM TO: A COMMON FIXED POINT THEOREM IN INTUITIONISTIC FUZZY METRIC SPACE USING SUBCOMPATIBLE MAPS"

The aim of this note is to point out a fallacy in the proof of Theorem 3.1 contained in the recent paper ( Int. J. Contemp. Math. Sci. 5 (2010), 2699-2707) proved in intuitionistic fuzzy metric spaces employing the newly introduced notion of sub-compatible pair of mappings wherein our claim is also substantiated with the aid of an appropriate example. We also rectify the erratic theorem in two ways.

Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation

We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.

On generalized weakly G-contraction mapping in G-metric spaces

In this paper, we establish some common fixed point results for two self-mappings f and g on a generalized metric space X. To prove our results we assume that f is a generalized weakly G-contraction mapping of types A and B with respect to g.

Extremal solutions and strong relaxation for nonlinear multivalued systems with maximal monotone terms

Abstract We consider differential systems in R N driven by a nonlinear nonhomogeneous second order differential operator, a maximal monotone term and a multivalued perturbation F ( t , u , u ′ ) . For periodic systems we prove the existence of extremal trajectories, that is solutions of the system in which F ( t , u , u ′ ) is replaced by ext F ( t , u , u ′ ) (= the extreme points of F ( t , u , u ′ ) ). For Dirichlet systems we show that the extremal trajectories approximate the solutions of the “convex” problem in the C 1 ( T , R N ) -norm (strong relaxation).

A general nonexistence result for inhomogeneous semilinear wave equations with double damping and potential terms

Abstract We investigate the large-time behavior of solutions for a class of inhomogeneous semilinear wave equations involving double damping and potential terms. Namely, we first establish a general criterium for the absence of global weak solutions. Next, some special cases of potential and inhomogeneous terms are studied. In particular, when the inhomogeneous term depends only on the variable space, the Fujita critical exponent and the second critical exponent in the sense of Lee and Ni are derived.

From Caristi’s Theorem to Ekeland’s Variational Principle in ${0}_{\sigma }$ -Complete Metric-Like Spaces

We discuss the extension of some fundamental results in nonlinear analysis to the setting of ${0}_{\sigma }$ -complete metric-like spaces. Then, we show that these extensions can be obtained via the corresponding results in standard metric spaces.

Clinical impact of the immunome in lymphoid malignancies: the role of Myeloid-Derived Suppressor Cells

The better definition of the mutual sustainment between neoplastic cells and immune system has been translated from the bench to the bedside acquiring value as prognostic factor. Additionally, it represents a promising tool for improving therapeutic strategies. In this context, myeloid-derived suppressor cells have gained a central role in tumor developing with consequent therapeutic implications. In this review, we will focus on the biological and clinical impact of the study of myeloid-derived suppressor cells in the settings of lymphoid malignancies.

MR3136553 Reviewed Popa, Valeriu; Patriciu, Alina-Mihaela A general fixed point theorem for pairs of mappings satisfying implicit relations in two G-metric spaces. An. Univ. Dunărea de Jos Galaţi Fasc. II Mat. Fiz. Mec. Teor. 4(35) (2012), no. 1-2, 22–28. (Reviewer: Calogero Vetro) 54H25 (47H10)

In [Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău No. 7 (1997), 127–133 (1999); MR1721711], V. Popa initiated the study of fixed points for mappings satisfying implicit relations as a way to unify and generalize various contractive conditions. Later on, many papers were published extending this approach to different metric settings. In the paper under review, the authors prove a result of such type for two mappings defined on two generalized metric spaces, called G-metric spaces and introduced by Z. Mustafa and B. Sims [J. Nonlinear Convex Anal. 7 (2006), no. 2, 289–297; MR2254125 (2007f:54049)].

Berinde mappings in orbitally complete metric spaces

Abstract We give a fixed point theorem for a self-mapping satisfying a general contractive condition of integral type in orbitally complete metric spaces. Some examples are given to illustrate our obtained result.

Graphical metric space: a generalized setting in fixed point theory

Building on recent ideas of Jachymski, we work on the notion of graphical metric space and prove an analogous result for the contraction mapping principle. In particular, the triangular inequality is replaced by a weaker one, which is satisfied by only those points which are situated on some path included in the graphical structure associated with the space. Some consequences, examples and an application to integral equations are presented to confirm the significance and unifying power of obtained generalizations.

Robin problems with general potential and double resonance

Abstract We consider a semilinear elliptic problem with Robin boundary condition and an indefinite and unbounded potential. The reaction term is a Caratheodory function exhibiting linear growth near ± ∞ . We assume that double resonance occurs with respect to any positive spectral interval. Using variational tools and critical groups, we show that the problem has a nontrivial smooth solution.

Multi-valued F-contractions and the solution of certain functional and integral equations

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

Some Integral Type Fixed-Point Theorems and an Application to Systems of Functional Equations

In this paper, we prove a new common fixed point theorem for four self mappings by using the notions of compatibility and subsequential continuity (alternate subcompatibility and reciprocal continuity) in metric spaces satisfying a general contractive condition of integral type. We give some examples to support the useability of our main result. Also, we obtain some fixed point theorems of Gregus type for four mappings satisfying a strict general contractive condition of integral type in metric spaces. We conclude the paper with an application of our main result to solvability of systems of functional equations.

Relaxation for a Class of Control Systems with Unilateral Constraints

We consider a nonlinear control system involving a maximal monotone map and with a priori feedback. We assume that the control constraint multifunction $U(t,x)$ is nonconvex valued and only lsc in the $x \in \mathbb{R}^{N}$ variable. Using the Q-regularization (in the sense of Cesari) of $U(t,\cdot )$, we introduce a relaxed system. We show that this relaxation process is admissible.

"Fixed Point Theorems for '?, ?'Contractive maps in Weak nonArchimedean Fuzzy Metric Spaces and Application"

The present study introduce the notion of (ψ, ϕ)-Contractive maps in weak non-Archimedean fuzzy metric spaces to derive a common fixed point theorem which complements and extends the main theorems of [C.Vetro, Fixed points in weak non-Archimedean fuzzy metric spaces, Fuzzy Sets and System, 162 (2011), 84-90] and [D.Mihet, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and System, 159 (2008) 739-744]. We support our result by establishing an application to product spaces.

Fixed point theorems for -contractive type mappings

Abstract In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.

Common fixed points of generalized Mizoguchi-Takahashi type contractions in partial metric spaces

We give some common fixed point results for multivalued mappings in the setting of complete partial metric spaces. Our theorems extend and complement analogous results in the existing literature on metric and partial metric spaces. Finally, we provide an example to illustrate the new theory.

Solution of an initial-value problem for parabolic equations via monotone operator methods

We study a general initial-value problem for parabolic equations in Banach spaces, by using a monotone operator method. We provide sufficient conditions for the existence of solution to such problem.

Existence and Relaxation Results for Second Order Multivalued Systems

AbstractWe consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have the combined effects of a maximal monotone term $A(x)$ A ( x ) and of a multivalued perturbation $F(t,x,y)$ F ( t , x , y ) which can be convex or nonconvex valued. We consider the cases where $D(A)\neq \mathbb{R}^{N}$ D ( A ) ≠ R N and $D(A)= \mathbb{R}^{N}$ D ( A ) = R N and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.

A note on some fundamental results in complete gauge spaces and application

We discuss the extension of some fundamental results in nonlinear analysis to the setting of gauge spaces. In particular, we establish Ekeland type and Caristi type results under suitable hypotheses for mappings and cyclic mappings. Our theorems generalize and complement some analogous results in the literature, also in the sense of ordered sets and oriented graphs. We apply our results to establishing the existence of solution to a second order nonlinear initial value problem.

Coupled fixed point results in cone metric spaces for -compatible mappings

In this paper, we introduce the concepts of -compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings F, G : X × X → X, where (X, d) is a cone metric space. We establish b-coupled coincidence and b-common coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al. [Appl. Math. Comput. 217, 195-202 (2010)]. Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered. 2010 Mathematics Subject Classificati…

Set-Valued Hardy-Rogers Type Contraction in 0-Complete Partial Metric Spaces

In this paper we introduce set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces and prove the corresponding theorem of fixed point. Our results generalize, extend, and unify several known results, in particular the recent Nadler’s fixed point theorem in the context of complete partial metric spaces established by Aydi et al. (2012). As an application of our results, a homotopy theorem for such mappings is derived. Also, some examples are included which show that our generalization is proper.

A Prototype of Wireless Sensor for Data Acquisition in Energy Management Systems

A prototype of a wireless sensor for monitoring electrical loads in a smart building is designed and implemented. The sensor can acquire the main electrical parameters of the connected load and, optionally, other physical quantities (e.g., room temperature). Unlike other wireless sensors in literature, the proposed sensor is cheap and small, exploits the Wi-Fi network that is commonly available inside buildings, and uses a lightweight message-based communication paradigm. Besides the sensor node, two management nodes are also implemented to manage sensor reconfiguration and the persistence of data. The measured data are stored in an SQLite database and can be used for various purposes, e.g.…

Semilinear Robin problems driven by the Laplacian plus an indefinite potential

We study a semilinear Robin problem driven by the Laplacian plus an indefinite potential. We consider the case where the reaction term f is a Carathéodory function exhibiting linear growth near ±∞. So, we establish the existence of at least two solutions, by using the Lyapunov-Schmidt reduction method together with variational tools.

Nonlinear contractions involving simulation functions in a metric space with a partial order

Very recently, Khojasteh, Shukla and Radenovic [F. Khojasteh, S. Shukla, S. Radenovic, Filomat, 29 (2015), 1189-1194] introduced the notion of Z-contraction, that is, a nonlinear contraction involving a new class of mappings namely simulation functions. This kind of contractions generalizes the Banach contraction and unifies several known types of nonlinear contractions. In this paper, we consider a pair of nonlinear operators satisfying a nonlinear contraction involving a simulation function in a metric space endowed with a partial order. For this pair of operators, we establish coincidence and common fixed point results. As applications, several related results in fixed point theory in a …

An approximate fixed point result for multivalued mappings under two constraint inequalities

We consider an approximate multivalued fixed point problem under two constraint inequalities, for which we provide sufficient conditions for the existence of at least one solution. Then, we present some consequences and related results.

Some notes on a second-order random boundary value problem

We consider a two-point boundary value problem of second-order random differential equation. Using a variant of the α-ψ-contractive type mapping theorem in metric spaces, we show the existence of at least one solution.

Singular Double Phase Problems with Convection

We consider a nonlinear Dirichlet problem driven by the sum of a $p$ -Laplacian and of a $q$ -Laplacian (double phase equation). In the reaction we have the combined effects of a singular term and of a gradient dependent term (convection) which is locally defined. Using a mixture of variational and topological methods, together with suitable truncation and comparison techniques, we prove the existence of a positive smooth solution.

Management of Venous Thromboembolism (VTE) in Patients with Acute Leukemia: Results from a Multicenter Study

Abstract Background In the last decades, evaluation of thrombotic complications secondary to acute leukemia (AL) has been poorly investigated. Only scant data are available on management and prevention of thrombosis in this setting. We performed a multicenter retrospective study with the aim to evaluate the management of venous thromboembolism (VTE) in patients with AL and to report the most commonly adopted regimens of treatment. Materials and methods Available clinical records of out and in-patients diagnosed with AL from January 2008 to June 2013 in 7 Reference Regional Hospitals were analyzed. Cases of VTE, including thrombosis in atypical sites [Retinal occlusion (RO) and Cerebral Sinu…

Common fixed point theorems for multi-valued maps

Abstract We establish some results on coincidence and common fixed points for a two-pair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.

Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence

We consider the Navier problem-Delta(2)(k,p)u(x)=f(x,u(x), del u(x), Delta u(x)) in Omega, u vertical bar(partial derivative Omega) =Delta u vertical bar(partial derivative Omega) = 0,driven by the sign-changing (degenerate) Kirchhoff type p(x)-biharmonic operator, and involving a (del u, Delta u)-dependent nonlinearity f. We prove the existence of solutions, in weak sense, defining an appropriate Nemitsky map for the nonlinearity. Then, the Brouwer fixed point theorem assessed for a Galerkin basis of the Banach space W-2,W-p(x)(Omega)boolean AND W-0(1,p(x))(Omega) leads to the existence result. The case of nondegenerate Kirchhoff type p(x)-biharmonic operator is also considered with respec…

A simulation function approach for best proximity point and variational inequality problems

We study sufficient conditions for existence of solutions to the global optimization problem min(x is an element of A) d(x, fx), where A, B are nonempty subsets of a metric space (X, d) and f : A -> B belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.

Management of venous thromboembolism in patients with acute leukemia at high bleeding risk: a multi-center study

In the last decades, evaluation of clinically relevant thrombotic complications in patients with acute leukemia (AL) has been poorly investigated. The authors performed a multi-center study to evaluate the management of symptomatic venous thromboembolism (VTE) in adult patients with AL. The intention was to find as clinically relevant the following: symptomatic Venous Thrombosis (VT) occurred in typical (lower limbs) and atypical (cerebral, upper limbs, abdominal, etc) sites with or without pulmonary embolism (PE). Over a population of 1461 patients with AL, 22 cases of symptomatic VTE were recorded in hospitalized patients with a mean age of 54.6 years. The absolute incidence of VTE was 1.…

Some coincidence and periodic points results in a metric space endowed with a graph and applications

The purpose of this paper is to obtain some coincidence and periodic points results for generalized $F$-type contractions in a metric space endowed with a graph. Some examples are given to illustrate the new theory. Then, we apply our results to establishing the existence of solution for a certain type of nonlinear integral equation.

Fixed point theory in partial metric spaces via φ-fixed point’s concept in metric spaces

Abstract Let X be a non-empty set. We say that an element x ∈ X is a φ-fixed point of T, where φ : X → [ 0 , ∞ ) and T : X → X , if x is a fixed point of T and φ ( x ) = 0 . In this paper, we establish some existence results of φ-fixed points for various classes of operators in the case, where X is endowed with a metric d. The obtained results are used to deduce some fixed point theorems in the case where X is endowed with a partial metric p. MSC:54H25, 47H10.

Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results

Abstract We give some fixed point theorems in the setting of metric spaces or partial metric spaces endowed with a finite number of graphs. The presented results extend and improve several well-known results in the literature. In particular, we discuss a Caristi type fixed point theorem in the setting of partial metric spaces, which has a close relation to Ekelandʼs principle.

Best proximity points for cyclic Meir–Keeler contractions

Abstract We introduce a notion of cyclic Meir–Keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic Meir–Keeler contractions. This theorem is a generalization of a recent result due to Eldred and Veeramani.

Multiple solutions with sign information for a (p,2)-equation with combined nonlinearities

Abstract We consider a parametric nonlinear Dirichlet problem driven by the sum of a p -Laplacian and of a Laplacian (a ( p , 2 ) -equation) and with a reaction which has the competing effects of two distinct nonlinearities. A parametric term which is ( p − 1 ) -superlinear (convex term) and a perturbation which is ( p − 1 ) -sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical p…

On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient

This paper is concerned with the nonexistence of global solutions to fractional in time nonlinear Schr&ouml

Solutions and positive solutions for superlinear Robin problems

We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.

Generalized (varphi,psi)-weak contractions involving (f,g)-reciprocally continuous maps in fuzzy metric spaces

We introduce the notion of (f,g)-reciprocal continuity in fuzzy metric spaces and prove a common fixed point theorem for a pair of sub-compatible maps by employing a generalized (varphi,psi)-weak contraction. As an application of our result, we prove a theorem for a (varphi,psi)-weak cyclic contraction in fuzzy metric spaces.

A fixed point theorem inG-metric spaces viaα-series

In the context of G -metric spaces we prove a common fixed point theorem for a sequence of self mappings using a new concept of α-series. Keywords: α-series, common fixed point, G -metric space Quaestiones Mathematicae 37(2014), 429-434

A remark on absolutely continuous functions in ℝ n

We introduce the notion ofα, λ-absolute continuity for functions of several variables and we compare it with the Hencl’s definition. We obtain that eachα, λ-absolutely continuous function isn, λ-absolutely continuous in the sense of Hencl and hence is continuous, differentiable almost everywhere and satisfies change of variables results based on a coarea formula and an area formula.

The class of F-contraction mappings with a measure of noncompactness

In this chapter we review a class of contraction conditions, which are largely used to obtain interesting generalizations of the Banach fixed-point theorem in various abstract settings. We also present a new fixed-point existence result obtained by considering such a kind of contraction condition and a measure of noncompactness. Moreover, we show the applicability of these results in the theory of functional equations.

Coupled fixed point theorems for symmetric (phi,psi)-weakly contractive mappings in ordered partial metric spaces

We establish some coupled fixed point theorems for symmetric (phi,chi)-weakly contractive mappings in ordered partial metric spaces. Some recent results of Berinde (Nonlinear Anal. 74 (2011), 7347-7355; Nonlinear Anal. 75 (2012), 3218-3228) and many others are extended and generalized to the class of ordered partial metric spaces.

Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential

Abstract We consider a two phase eigenvalue problem driven by the ( p , q ) -Laplacian plus an indefinite and unbounded potential, and Robin boundary condition. Using a modification of the Nehari manifold method, we show that there exists a nontrivial open interval I ⊆ R such that every λ ∈ I is an eigenvalue with positive eigenfunctions. When we impose additional regularity conditions on the potential function and the boundary coefficient, we show that we have smooth eigenfunctions.

Singular (p, q)-equations with superlinear reaction and concave boundary condition

We consider a parametric nonlinear elliptic problem driven by the sum of a p-Laplacian and of a q-Laplacian (a (Formula presented.) -equation) with a singular and (Formula presented.) -superlinear reaction and a Robin boundary condition with (Formula presented.) -sublinear boundary term (Formula presented.). So, the problem has the combined effects of singular, concave and convex terms. We look for positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.

MR3269340 Reviewed O'Regan, Donal Lefschetz type theorems for a class of noncompact mappings. J. Nonlinear Sci. Appl. 7 (2014), no. 5, 288–295. (Reviewer: Calogero Vetro) 47H10

Lefschetz fixed-point theorem furnishes a way for counting the fixed points of a suitable mapping. In particular, the Lefschetz fixed-point theorem states that if Lefschetz number is not zero, then the involved mapping has at least one fixed point, that is, there exists a point that does not change upon application of mapping. ewline Let $f={f_q}:E o E$ be an endomorphism of degree zero of graded vector space $E={E_q}$. Let $ ilde{E}=E setminus {x in E : f^n(x)=0, mbox{ for some }n in mathbb{N}}$. Define the generalized Lefschetz number $Lambda(f)$ by $$Lambda(f)=sum_{q geq 0}(-1)^qmbox{Tr}(f_q),$$ where $mbox{Tr}(f)=mbox{tr}( ilde{f})$ is the generalized trace of $f$, ``tr'' is the ordinar…

A multiplicity theorem for parametric superlinear (p,q)-equations

We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.

Some new fixed point results in non-Archimedean fuzzy metric spaces

In this paper, we introduce the notions of fuzzy $(\alpha,\beta,\varphi)$-contractive mapping, fuzzy $\alpha$-$\phi$-$\psi$-contractive mapping and fuzzy $\alpha$-$\beta$-contractive mapping and establish some results of fixed point for this class of mappings in the setting of non-Archimedean fuzzy metric spaces. The results presented in this paper generalize and extend some recent results in fuzzy metric spaces. Also, some examples are given to support the usability of our results.

Common fixed point theorems for mappings satisfying common property (E.A.) in symmetric spaces

In this paper, common fixed point theorems for mappings satisfying a generalized contractive condition are obtained in symmetric spaces by using the notion of common property (E.A.). In the process, a host of previously known results are improved and generalized. We also derive results on common fixed point in probabilistic symmetric spaces.

Fixed point theorems for non-self mappings in symmetric spaces under φ-weak contractive conditions and an application to functional equations in dynamic programming

In this paper, we prove some common fixed point theorems for two pairs of non-self weakly compatible mappings enjoying common limit range property, besides satisfying a generalized phi-weak contractive condition in symmetric spaces. We furnish some illustrative examples to highlight the realized improvements in our results over the corresponding relevant results of the existing literature. We extend our main result to four finite families of mappings in symmetric spaces using the notion of pairwise commuting mappings. Finally, we utilize our results to discuss the existence and uniqueness of solutions of certain system of functional equations arising in dynamic programming.

Caristi Type Selections of Multivalued Mappings

Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems.

Tripled Fixed Point Results for T-Contractions on Abstract Metric Spaces

In this paper we introduce the notion of T-contraction for tripled fi xed points in abstract metric spaces and obtain some tripled fi xed point theorems which extend and generalize well-known comparable results in the literature. To support our results, we present an example and an application to integral equations.

Common fixed points of generalized contractions on partial metric spaces and an application

Abstract In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778–2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given.

Common fixed points of mappings satisfying implicit relations in partial metric spaces

Matthews, [S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197], introduced and studied the concept of partial metric space, as a part of the study of denotational semantics of dataflow networks. He also obtained a Banach type fixed point theorem on complete partial metric spaces. Very recently Berinde and Vetro, [V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory and Applications 2012, 2012:105], discussed, in the setting of metric and ordered metric spaces, coincidence point and common fixed point theorems fo…

On the existence of at least a solution for functional integral equations via measure of noncompactness

In this article, we use fixed-point methods and measure of noncompactness theory to focus on the problem of establishing the existence of at least a solution for the following functional integral equation ¶ \[u(t)=g(t,u(t))+\int_{0}^{t}G(t,s,u(s))\,ds,\quad t\in{[0,+\infty[},\] in the space of all bounded and continuous real functions on $\mathbb{R}_{+}$ , under suitable assumptions on $g$ and $G$ . Also, we establish an extension of Darbo’s fixed-point theorem and discuss some consequences.

Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations

We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.

A note on best proximity point theory using proximal contractions

In this paper, a reduction technique is used to show that some recent results on the existence of best proximity points for various classes of proximal contractions can be concluded from the corresponding results in fixed point theory.

Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces

Abstract We prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces. As application of the presented results, we give a unique fixed point result for a mapping satisfying a weak cyclical contractive condition. We also provide some illustrative examples. MSC:47H10, 54H25.

A singular (p,q)-equation with convection and a locally defined perturbation

Abstract We consider a parametric Dirichlet problem driven by the ( p , q ) -Laplacian and a reaction which is gradient dependent (convection) and the competing effects of two more terms, one a parametric singular term and a locally defined perturbation. We show that for all small values of the parameter the problem has a positive smooth solution.

Variable exponent p(x)-Kirchhoff type problem with convection

Abstract We study a nonlinear p ( x ) -Kirchhoff type problem with Dirichlet boundary condition, in the case of a reaction term depending also on the gradient (convection). Using a topological approach based on the Galerkin method, we discuss the existence of two notions of solutions: strong generalized solution and weak solution. Strengthening the bound on the Kirchhoff type term (positivity condition), we establish existence of weak solution, this time using the theory of operators of monotone type.

Fixed point theorems for $\alpha$-$\psi$-contractive type mappings

In this paper, we introduce a new concept of $\alpha$-$\psi$-contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.

Constant sign and nodal solutions for nonlinear robin equations with locally defined source term

We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

A homotopy fixed point theorem in 0-complete partial metric space

We generalize a result of Feng and Liu, on multi-valued contractive mappings, for studying the relationship between fixed point sets and homotopy fixed point sets. The presented results are discussed in the generalized setting of 0-complete partial metric spaces. An example and a nonlinear alternative of Leray-Schauder type are given to support our theorems.

Fixed point iterative schemes for variational inequality problems

In a wide class of evolutionary processes, the problem of computing the solutions of an initial value problem is encountered. Here, we consider projected dynamical systems in the sense of \cite{Daniele} and references therein. Precisely, a projected dynamical system is an operator which solves the initial value problem: \begin{equation}\label{PDS}\frac{dx(t)}{dt}= \Pi_{\mathbb{K}}\left(x(t),-F(x(t))\right), \quad x(0)=x_0 \in \mathbb{K}, \, t \in [0,+\infty[,\tag{P}\end{equation} where $\mathbb{K}$ is a convex polyhedral set in $\mathbb{R}^n$, $F: \mathbb{K} \to \mathbb{R}^n$ and $\Pi_{\mathbb{K}}: \mathbb{R} \times \mathbb{K} \to \mathbb{R}^n$ is given as follows $\Pi_{\mathbb{K}}(x,-F(x))…

On the critical curve for systems of hyperbolic inequalities in an exterior domain of the half-space

We establish blow-up results for a system of semilinear hyperbolic inequalities in an exterior domain of the half-space. The considered system is investigated under an inhomogeneous Dirichlet-type boundary condition depending on both time and space variables. In certain cases, an optimal criterium of Fujita-type is derived. Our results yield naturally sharp nonexistence criteria for the corresponding stationary wave system and equation.

A New Extension of Darbo's Fixed Point Theorem Using Relatively Meir-Keeler Condensing Operators

We consider relatively Meir–Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. [‘Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness’, Acta Math. Sci. Ser. B35 (2015), 552–566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations.

Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application of functional equations in dynamic programming

In this paper, we prove some integral type common fixed point theorems for weakly compatible mappings in Non-Archimedean Menger PM-spaces employing common property (E.A). Some examples are furnished which demonstrate the validity of our results. We extend our main result to four finite families of self-mappings employing the notion of pairwise commuting. Moreover, we give an application which supports the usability of our main theorem.

Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential

AbstractWe consider a parametric nonlinear Robin problem driven by the negativep-Laplacian plus an indefinite potential. The equation can be thought as a perturbation of the usual eigenvalue problem. We consider the case where the perturbation$$f(z,\cdot )$$f(z,·)is$$(p-1)$$(p-1)-sublinear and then the case where it is$$(p-1)$$(p-1)-superlinear but without satisfying the Ambrosetti–Rabinowitz condition. We establish existence and uniqueness or multiplicity of positive solutions for certain admissible range for the parameter$$\lambda \in {\mathbb {R}}$$λ∈Rwhich we specify exactly in terms of principal eigenvalue of the differential operator.

Nonlinear vector Duffing inclusions with no growth restriction on the orientor field

We consider nonlinear multivalued Dirichlet Duffing systems. We do not impose any growth condition on the multivalued perturbation. Using tools from the theory of nonlinear operators of monotone type, we prove existence theorems for the convex and the nonconvex problems. Also we show the existence of extremal trajectories and show that such solutions are $C_0^1(T,\mathbb{R}^N)$-dense in the solution set of the convex problem (strong relaxation theorem).

On the critical behavior for inhomogeneous wave inequalities with Hardy potential in an exterior domain

Abstract We study the wave inequality with a Hardy potential ∂ t t u − Δ u + λ | x | 2 u ≥ | u | p in  ( 0 , ∞ ) × Ω , $$\begin{array}{} \displaystyle \partial_{tt}u-{\it\Delta} u+\frac{\lambda}{|x|^2}u\geq |u|^p\quad \mbox{in } (0,\infty)\times {\it\Omega}, \end{array}$$ where Ω is the exterior of the unit ball in ℝ N , N ≥ 2, p > 1, and λ ≥ − N − 2 2 2 $\begin{array}{} \displaystyle \left(\frac{N-2}{2}\right)^2 \end{array}$ , under the inhomogeneous boundary condition α ∂ u ∂ ν ( t , x ) + β u ( t , x ) ≥ w ( x ) on  ( 0 , ∞ ) × ∂ Ω , $$\begin{array}{} \displaystyle \alpha \frac{\partial u}{\partial \nu}(t,x)+\beta u(t,x)\geq w(x)\quad\mbox{on } (0,\infty)\times \partial{\it\Omega}, \e…

A fixed point theorem for a Meir-Keeler type contraction through rational expression

In this paper, we establish a new fixed point theorem for a Meir-Keeler type contraction through rational expression. The presented theorem is an extension of the result of Dass and Gupta (1975). Some applications to contractions of integral type are given.

The existence of best proximity points in metric spaces with the property UC

Abstract Eldred and Veeramani in [A.A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001–1006. MR2260159] proved a theorem which ensures the existence of a best proximity point of cyclic contractions in the framework of uniformly convex Banach spaces. In this paper we introduce a notion of the property UC and extend the Eldred and Veeramani theorem to metric spaces with the property UC.

A fixed point theorem for (varphi,L)-weak contraction mappings on a partial metric space

In this paper, we explore (varphi,L)-weak contractions of Berinde by obtaining Suzuki-type fixed point results. Thus, we obtain generalized fixed point results for Kannan's, Chatterjea's and Zamfirescu's mappings on a 0-complete partial metric space. In this way we obtain very general fixed point theorems that extend and generalize several related results from the literature.

Best proximity points: Convergence and existence theorems for p-cyclic mappings

Abstract We introduce a new class of mappings, called p -cyclic φ -contractions, which contains the p -cyclic contraction mappings as a subclass. Then, convergence and existence results of best proximity points for p -cyclic φ -contraction mappings are obtained. Moreover, we prove results of the existence of best proximity points in a reflexive Banach space. These results are generalizations of the results of Al-Thagafi and Shahzad (2009) [8] .

phi-Best proximity point theorems and applications to variational inequality problems

The main concern of this study is to introduce the notion of $$\varphi $$ -best proximity points and establish the existence and uniqueness of $$\varphi $$ -best proximity point for non-self mappings satisfying $$(F,\varphi )$$ -proximal and $$(F,\varphi )$$ -weak proximal contraction conditions in the context of complete metric spaces. Some examples are supplied to support the usability of our results. As applications of the obtained results, some new best proximity point results in partial metric spaces are presented. Furthermore, sufficient conditions to ensure the existence of a unique solution for a variational inequality problem are also discussed.

On a Robin (p,q)-equation with a logistic reaction

We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation) plus an indefinite potential term and a parametric reaction of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter \(\lambda \gt 0\) varies. Also, we show that for every admissible parameter \(\lambda \gt 0\), the problem admits a smallest positive solution.

Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems

We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is $$(p-1)$$-superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter $$\lambda >0$$ varies. Also we prove the existence of a minimal positive solution $$u_\lambda ^*$$ and determine the monotonicity and continuity properties of the map $$\lambda \rightarrow u_\lambda ^*$$.

(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms

We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian ($$p>2$$) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric $$(p-1)$$-linear term which is resonant as $$x \rightarrow - \infty $$, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.

Prognostic assessment and treatment of primary gastric lymphomas: how endoscopic ultrasonography can help in tailoring patient management.

Endoscopic ultrasonography (EUS) has recently gained a pivotal role in the management of gastric lymphomas, especially in the diagnostic workup. Its accuracy and reliability have overcome those of other imaging techniques, such that it represents an invaluable tool for the management of gastric lymphomas. Although this technique is operator dependent, its application in large series has proved its reliability. Thus, it has generally been considered a useful tool for providing information crucial in deciding the treatment program, especially for mucosa-associated lymphoid tissue (MALT) lymphomas, for which EUS can provide an accurate evaluation of disease extension and treatment response pro…

Fixed point theory for cyclic weak ϕ-contraction in fuzzy metric spaces

In this paper, we introduce cyclic weak $\phi-$contractions in fuzzy metric spaces and utilize the same to prove some results on existence and uniqueness of fixed point in fuzzy metric spaces. Some related results are also proved besides furnishing illustrative examples.

On Noncoercive (p, q)-Equations

We consider a nonlinear Dirichlet problem driven by a (p, q)-Laplace differential operator (1 < q < p). The reaction is (p - 1)-linear near +/-infinity and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q = 2, we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.

Some fixed point theorems for generalized contractive mappings in complete metric spaces

We introduce new concepts of generalized contractive and generalized alpha-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on complete metric spaces and b-complete b-metric spaces. Our results extend the theorems of Ciric, Chatterjea, Kannan and Reich.

Common fixed point theorems in fuzzy metric spaces employing CLR_{S} and JCLR_{ST} properties

In this paper, we utilize the $CLR_{S}$ and $JCLR_{ST}$ properties to prove some existence theorems of common fixed point for contractive mappings in fuzzy metric spaces. Our results generalize and extend many known results from the literature. An example and some applications are given to show the usability of the presented results.

An Integral Version of Ćirić’s Fixed Point Theorem

We establish a new fixed point theorem for mappings satisfying a general contractive condition of integral type. The presented theorem generalizes the well known Ciric's fixed point theorem [Lj. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (26) (1971) 19-26]. Some examples and applications are given.

A Perturbed Cauchy Viscoelastic Problem in an Exterior Domain

A Cauchy viscoelastic problem perturbed by an inverse-square potential, and posed in an exterior domain of RN, is considered under a Dirichlet boundary condition. Using nonlinear capacity estimates specifically adapted to the non-local nature of the problem, the potential function and the boundary condition, we establish sufficient conditions for the nonexistence of weak solutions.

Coincidence and common fixed points of weakly reciprocally continuous and compatible hybrid mappings via an implicit relation and an application

Using the hybrid version of the notion of weakly reciprocal continuous mappings due to Gairola et al. [Coincidence and fixed point for weakly reciprocally continuous single-valued and multi-valued maps, Demonstratio Math. (2013/2014), accepted], we prove a coincidence and common fixed point theorem for a hybrid pair of compatible mappings via an implicit relation. Our main result improves and generalizes a host of previously known theorems. As an application, we give a homotopy theorem which supports our main result.

Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces

The purpose of this paper is to present some fixed point theorems for T -weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations.

Solvability of integrodifferential problems via fixed point theory in b-metric spaces

The purpose of this paper is to study the existence of solutions set of integrodifferential problems in Banach spaces. We obtain our results by using fixed point theorems for multivalued mappings, under new contractive conditions, in the setting of complete b-metric spaces. Also, we present a data dependence theorem for the solutions set of fixed point problems.

Sulla K-variazione Essenziale di Una Funzione reale

In this paper we consider a definition of essentialK-variation for real functions which gives information on the absolute integrability of its approximate derivate on a measurable set.

Arginase 1 Is a Marker of Myeloid-Mediated Immunosuppression with Prognostic Meaning in Classic Hodgkin Lymphoma

Abstract Purpose : Neutrophilia is hallmark of classic Hodgkin Lymphoma (cHL), but its precise characterization remains elusive. We aimed at investigating the immunosuppressive role of high-density neutrophils in HL. Experimental design : First, N-HL function was evaluated in vitro, showing increased arginase (Arg-1) expression and activity compared to healthy subjects. Second, we measured serum level of Arg-1 (s-Arg-1) by ELISA in two independent, training (N=40) and validation (N=78) sets. Results : s-Arg-1 was higher in patients with advanced stage (p=0.045), B-symptoms (p=0.0048) and a positive FDG-PET scan after two cycles of chemotherapy (PET-2, p=0.012). Baseline levels of s-Arg-1 &g…

Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …

Fixed point theorems for fuzzy mappings and applications to ordinary fuzzy differential equations

Abstract Ran and Reurings (Proc. Am. Math. Soc. 132(5):1435-1443, 2004) proved an analog of the Banach contraction principle in metric spaces endowed with a partial order and discussed some applications to matrix equations. The main novelty in the paper of Ran and Reurings involved combining the ideas in the contraction principle with those in the monotone iterative technique. Motivated by this, we present some common fixed point results for a pair of fuzzy mappings satisfying an almost generalized contractive condition in partially ordered complete metric spaces. Also we give some examples and an application to illustrate our results. MSC:46S40, 47H10, 34A70, 54E50.

A model of capillary phenomena in RN with subcritical growth

This paper deals with the nonlinear Dirichlet problem of capillary phenomena involving an equation driven by the p-Laplacian-like di¤erential operator in RN. We prove the existence of at least one nontrivial nonnegative weak solution, when the reaction term satisfies a sub-critical growth condition and the potential term has certain regularities. We apply the energy functional method and weaker compactness conditions.

Fixed point results for α-implicit contractions with application to integral equations

Recently, Aydi et al. [On fixed point results for α-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21(1):40–56, 2016] proved some fixed point results involving α-implicit contractive conditions in quasi-b-metric spaces. In this paper we extend and improve these results and derive some new fixed point theorems for implicit contractions in ordered quasi-b-metric spaces. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces

Abstract In this paper, we obtain a Suzuki type fixed point theorem for a generalized multivalued mapping on a partial Hausdorff metric space. As a consequence of the presented results, we discuss the existence and uniqueness of the bounded solution of a functional equation arising in dynamic programming.

(φ, ψ)-weak contractions in intuitionistic fuzzy metric spaces

The purpose of this paper is to extend the notion of (phi,psi)-weak contraction to intuitionistic fuzzy metric spaces, by using an altering distance function. We obtain common fixed point results in intuitionistic fuzzy metric spaces, which generalize several known results from the literature.

On a theorem of Khan in a generalized metric space

Existence and uniqueness of fixed points are established for a mapping satisfying a contractive condition involving a rational expression on a generalized metric space. Several particular cases and applications as well as some illustrative examples are given.

Multiple solutions for strongly resonant Robin problems

We consider nonlinear (driven by the p†Laplacian) and semilinear Robin problems with indefinite potential and strong resonance with respect to the principal eigenvalue. Using variational methods and critical groups, we prove four multiplicity theorems producing up to four nontrivial smooth solutions.

A local notion of absolute continuity in IR^n

We consider the notion of p, δ-absolute continuity for functions of several variables introduced in [2] and we investigate the validity of some basic properties that are shared by absolutely continuous functions in the sense of Maly. We introduce the class $δ−BV^p_loc(\Omega,IR^m)$ and we give a characterization of the functions belonging to this class.

Cyclic admissible contraction and applications to functional equations in dynamic programming

In this paper, we introduce the notion of T-cyclic $( \alpha ,\beta ) $ -contraction and give some common fixed point results for this type of contractions. The presented theorems extend, generalize, and improve many existing results in the literature. Several examples and applications to functional equations arising in dynamic programming are also given in order to illustrate the effectiveness of the obtained results.

A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations

We investigate the existence of fixed points of self-mappings via simulation functions and measure of noncompactness. We use different classes of additional functions to get some general contractive inequalities. As an application of our main conclusions, we survey the existence of a solution for a class of integral equations under some new conditions. An example will be given to support our results.

Fixed points for multivalued mappings in b-metric spaces

In 2012, Samet et al. introduced the notion ofα-ψ-contractive mapping and gave sufficient conditions for the existence of fixed points for this class of mappings. The purpose of our paper is to study the existence of fixed points for multivalued mappings, under anα-ψ-contractive condition of Ćirić type, in the setting of completeb-metric spaces. An application to integral equation is given.

Learning to Navigate in the Gaussian Mixture Surface

In the last years, deep learning models have achieved remarkable generalization capability on computer vision tasks, obtaining excellent results in fine-grained classification problems. Sophisticated approaches based-on discriminative feature learning via patches have been proposed in the literature, boosting the model performances and achieving the state-of-the-art over well-known datasets. Cross-Entropy (CE) loss function is commonly used to enhance the discriminative power of the deep learned features, encouraging the separability between the classes. However, observing the activation map generated by these models in the hidden layer, we realize that many image regions with low discrimin…

A remark on absolutely continuous functions in IR^n

We introduce the notion of α, λ-absolute continuity for functions of several variables and we compare it with the Hencl’s definition. We obtain that each α,λ-absolutely continuous function is n, λ-absolutely continuous in the sense of Hencl and hence is continuous, differentiable almost everywhere and satisfies change of variables results based on a coarea formula and an area formula.

Fixed points in weak non-Archimedean fuzzy metric spaces

Mihet [Fuzzy $\psi$-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 159 (2008) 739-744] proved a theorem which assures the existence of a fixed point for fuzzy $\psi$-contractive mappings in the framework of complete non-Archimedean fuzzy metric spaces. Motivated by this, we introduce a notion of weak non-Archimedean fuzzy metric space and prove that the weak non-Archimedean fuzzy metric induces a Hausdorff topology. We utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings.

Fixed point results under generalized c-distance with application to nonlinear fourth-order differential equation

We consider the notion of generalized c-distance in the setting of ordered cone b-metric spaces and obtain some new fixed point results. Our results provide a more general statement, under which can be unified some theorems of the existing literature. In particular, we refer to the results of Sintunavarat et al. [W. Sintunavarat, Y.J. Cho, P. Kumam, Common fixed point theorems for c-distance in ordered cone metric spaces, Comput. Math. Appl. 62 (2011) 1969-1978]. Some examples and an application to nonlinear fourth-order differential equation are given to support the theory.

Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth

We consider a nonlinear elliptic problem driven by the Dirichlet $p$-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term $f(z, \cdot,y)$. Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution.

Applying fuzzy Particle Swarm Optimization to Multi-unit Double Auctions

Abstract In the context of Quadratic Programming Problems, we use a fuzzy Particle Swarm Optimization (PSO) algorithm to analyze a Multi-unit Double Auction (MDA) market. We give also a Linear Programming (LP) based upper bound to help the decision maker in dealing with constraints in the mathematical model. In the computational study, we evaluate our algorithm and show that it is a feasible approach for processing bids and calculating assignments.

Nonexistence of solutions to higher order evolution inequalities with nonlocal source term on Riemannian manifolds

We establish sufficient conditions for the nonexistence of nontrivial solutions to higher order evolution inequalities, with respect to the time variable. We consider a nonlocal source term, and work on complete noncompact Riemannian manifolds. The obtained conditions depend on the parameters of the problem and the geometry of the manifold. Our main result recovers some nonexistence theorems from the literature, established in the whole Euclidean space.

On modified α-ϕ-fuzzy contractive mappings and an application to integral equations

Abstract We introduce the notion of a modified α-ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory.

Parametric nonlinear singular Dirichlet problems

Abstract We consider a nonlinear parametric Dirichlet problem driven by the p -Laplacian and a reaction which exhibits the competing effects of a singular term and of a resonant perturbation. Using variational methods together with suitable truncation and comparison techniques, we prove a bifurcation-type theorem describing the dependence on the parameter of the set of positive solutions.

Edelstein-Suzuki-type resuls for self-mappings in various abstract spaces with application to functional equations

Abstract The fixed point theory provides a sound basis for studying many problems in pure and applied sciences. In this paper, we use the notions of sequential compactness and completeness to prove Eldeisten-Suzuki-type fixed point results for self-mappings in various abstract spaces. We apply our results to get a bounded solution of a functional equation arising in dynamic programming.

SOLUTION TO RANDOM DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS

We study a family of random differential equations with boundary conditions. Using a random fixed point theorem, we prove an existence theorem that yields a unique random solution.

Common fixed point theorems for families of occasionally weakly compatible mappings

We prove some common fixed point theorems in probabilistic semi-metric spaces for families of occasionally weakly compatible mappings. We also give a common fixed point theorem for mappings satisfying an integral-type implicit relation.

Further generalization of fixed point theorems in Menger PM-spaces

In this work, we establish some fixed point theorems by revisiting the notion of ψ-contractive mapping in Menger PM-spaces. One of our results (namely, Theorem 2.3) may be viewed as a possible answer to the problem of existence of a fixed point for generalized type contractive mappings in M-complete Menger PM-spaces under arbitrary t-norm. Some examples are furnished to demonstrate the validity of the obtained results.

Common fixed points in ordered Banach spaces

In this paper we introduce the notion of g-weak isotone mappings in an ordered Banach space and we extend some common fixed point theorems of Dhage, O’Regan and Agarwal

A Coupled Fixed Point Theorem in Fuzzy Metric Space Satisfying ϕ-Contractive Condition

The intent of this paper is to prove a coupled fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous) mappings, satisfyingϕ-contractive conditions in a fuzzy metric space. We also furnish some illustrative examples to support our results.

Endoscopic ultrasonography in gastric lymphomas: appraisal on reliability in long-term follow-up

The reliability of endoscopic ultrasonography (EUS) in follow-up management of gastric lymphomas has not been clearly validated. We conducted a retrospective analysis on 23 patients, 12 affected by mucosa-associated lymphoid tissue (MALT) lymphoma, eight by diffuse large B-cell lymphoma, and three by high-grade lymphoma with low-grade component, all treated with a stomach-conservative approach. One hundred and twenty matched evaluations with both EUS and endoscopy with biopsy (E-Bx) were performed, according to validated guidelines and clinical judgment. At a median follow-up of 87 months ranged between 9.5 and 166 months, the analysis of progression-free survival and disease-free survival …

Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness

This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book's central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscel…