MR2819034 Castillo, René Erlín The Nemytskii operator on bounded p-variation in the mean spaces. Mat. Enseñ. Univ. (N. S.) 19 (2011), no. 1, 31–41. (Reviewer: Pasquale Vetro)

The author introduces the notion of bounded $p$-variation in the sense of $L_p$-norm. Precisely: Let $f \in L_p[0,2\pi]$ with $1<p<\infty$. Let $P: 0=t_0 <t_1< \cdots <t_n=2\pi$ be a partion of $[0,2\pi]$ if $$V_p^m(f,T) = \sup \{\sum_{k=1} ^{n}\int_T\frac{|f(x+t_k)-f(x+t_{k-1})|^p)}{|t_k-t_{k-1}|^{p-1}}\}< \infty,$$ where the supremum is taken over all partitions $P$ of $[0,2\pi]$ and $T=\mathbb{R}/2\pi \mathbb{Z}$, then $f$ is said to be of bounded $p$-variation in the mean. The author obtains a Riesz type result for functions of bounded $p$-variation in the mean and gives some properties for functions of bounded $p$-variation by using the Nemytskii operator.

Existence of fixed point for GP(Λ;Θ)-contractive mappings in GP-metric spaces

We combine some classes of functions with a notion of hybrid $GP_{(\Lambda,\Theta )}$ - $H$ - $F$ - contractive mapping for establishing some  fixed point results in the setting of $GP$-metric spaces. An illustrative example  supports the new theory.

COMMON FIXED POINTS FOR psi-CONTRACTIONS ON PARTIAL METRIC SPACES

We prove some generalized versions of an interesting result of Matthews using conditions of different type in 0-complete partial metric spaces. We give, also, a homotopy result for operators on partial metric spaces.

MR2684111 Kadelburg, Zoran; Radenović, Stojan; Rakočević, Vladimir Topological vector space-valued cone metric spaces and fixed point theorems. Fixed Point Theory Appl. 2010, Art. ID 170253, 17 pp. (Reviewer: Pasquale Vetro)

Recently, Huang and Zhang [\emph{Cone metric spaces and fixed point theorems of contractive mappings}, J. Math. Anal. Appl., \textbf{332} (2007), 1468 -1476] defined cone metric spaces by substituing an order normed space for the real numbers and proved some fixed point theorems. Let $E$ be a real Hausdorff topological vector space and $P$ a cone in $E$ with int\,$P\neq \emptyset$, where int\,$P$ denotes the interior of $P$. Let $X$ be a nonempty set. A function $d : X \times X\to E$ is called a \emph{tvs}-cone metric and $(X, d)$ is called a \emph{tvs}-cone metric space, if the following conditions hold: (1) $\theta \leq d(x, y)$ for all $x, y \in X$ and $d(x, y)= \theta$ if and only if $x…

Some new extensions of Edelstein-Suzuki-type fixed point theorem to G-metric and G-cone metric spaces

Abstract In this paper, we prove some fixed point theorems for generalized contractions in the setting of G -metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74–79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317]. We prove, also, a fixed point theorem in the setting of G -cone metric spaces.

Nonlinear quasi-contractions of Ciric type

In this paper we obtain points of coincidence and common fixed points for two self mappings satisfying a nonlinear contractive condition of Ciric type. As application, using the scalarization method of Du, we deduce a result of common fixed point in cone metric spaces.

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.

Fixed point results on metric-type spaces

Abstract In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.

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.

Approximation of fixed points of asymptotically g-nonexpansive mapping

A result of Suzuki type in partial G-metric spaces

Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial …

Fixed point theorems for α-set-valued quasi-contractions in b-metric spaces

Recently, Samet et al. [B. Samet, C. Vetro and P. Vetro, Fixed point theorems for alpha-psi-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165] 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 notions of alpha-set-valued contraction and alpha-set-valued quasi-contraction and we give some fixed point theorems for such classes of mappings in the setting of b-metric spaces and ordered b-metric spaces. The presented theorems extend, unify and generalize several well-known comparable results in the existing literature.

Common fixed points for self mappings on compact metric spaces

In this paper we obtain a result of existence of points of coincidence and of common fixed points for two self mappings on compact metric spaces satisfying a contractive condition of Suzuki type. We also present some examples to illustrate our results. Moreover, using the scalarization method of Du, we deduce a result of common fixed point in compact cone metric spaces.

Common fixed points in cone metric spaces for $MK$-pairs and $L$-pairs

In this paper we introduce some contractive conditions of Meir-Keeler type for a pair of mappings, called $MK$-$pair$ and $L\textrm{-}pair$, in the framework of cone metric spaces and we prove theorems which assure existence and uniqueness of common fixed points for $MK$-$pairs$ and $L \textrm{-}pairs$. As an application we obtain a result of common fixed point of a $p$-$MK$-pair, a mapping and a multifunction, in complete cone metric spaces. These results extend and generalize well-known comparable results in the literature.

MR2789279 Aziz, Wadie; Leiva, Hugo; Merentes, Nelson; Rzepka, Beata A representation theorem for φ-bounded variation of functions in the sense of Riesz. Comment. Math. 50 (2010), no. 2, 109–120. (Reviewer: Pasquale Vetro)

The authors consider the class $V_\varphi^R (I^b_a)$ of functions $f:I^b_a =[a_1,b_1]\times [a_2,b_2]\subset \mathbb{R}^2 \to \mathbb{R}$ with bounded $\varphi$-total variation in the sense of Riesz, where $\varphi: [0,+ \infty) \to [0,+ \infty)$ is nondecreasing and continuous with $\varphi(0)=0$ and $\varphi(t) \to +\infty$ as $t \to +\infty$. If we assume that $\varphi$ is also such that $\lim_{t \to +\infty}\frac{\varphi(t)}{t}= +\infty$, then we obtain the main result. Precisely, the authors give a characterization of function of two variables defined on a rectangle $I^b_a$ belonging to $V_\varphi^R (I^b_a)$. Clearly, this result is a generalization of the Riesz Lemma.

MR3136895 Reviewed Ray, S.; Garai, A. The Laplace derivative. Math. Student 81 (2012), no. 1-4, 171–175. (Reviewer: Pasquale Vetro) 26A24

In this paper the authors consider the Laplace derivative of a real function of a real variable introduced by R. E. Svetic [Comment. Math. Univ. Carolin. 42 (2001), no. 2, 331–343; MR1832151 (2002d:26008)]. The aim of this paper is to study the properties of the first-order Laplace derivative. They also prove Rolle's theorem, Darboux's theorem and other such theorems for the Laplace derivative.

Common fixed points in generalized metric spaces

Abstract We establish some common fixed point theorems for mappings satisfying a ( ψ , φ ) -weakly contractive condition in generalized metric spaces. Presented theorems extend and generalize many existing results in the literature.

Fixed point results for Gm-Meir-Keeler contractive and G-(α,ψ)-Meir-Keeler contractive mappings

MR2670689 Rezapour, Shahram; Khandani, Hassan; Vaezpour, Seyyed M. Efficacy of cones on topological vector spaces and application to common fixed points of multifunctions. Rend. Circ. Mat. Palermo (2) 59 (2010), no. 2, 185–197. (Reviewer: Pasquale Vetro)

Recently, Huang and Zhang defined cone metric spaces by substituting an order normed space for the real numbers and proved some fixed point theorems. For fixed point results in the framework of cone metric space see, also, Di Bari and Vetro [\textit{$\varphi$-pairs and common fixed points in cone metric spaces}, Rend. Circ. Mat. Palermo \textbf{57} (2008), 279--285 and \textit{Weakly $\varphi$-pairs and common fixed points in cone metric spaces}, Rend. Circ. Mat. Palermo \textbf{58} (2009), 125--132]. Let $(E,\tau)$ be a topological vector space and $P$ a cone in $E$ with int\,$P\neq \emptyset$, where int\,$P$ denotes the interior of $P$. The authors define a topology $\tau_p$ on $E$ so tha…

$varphi$-pairs and common fixed points in cone metric spaces

In this paper we introduce a contractive condition, called $\varphi \textrm{-}pair$, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for $\varphi \textrm{-}pairs$. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.

Weakly \varphi-pairs and common fixed points in cone metric spaces

In this paper we introduce a weak contractive condition, called weakly \varphi-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which ensures existence and uniqueness of common fixed points for such mappings. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.

Approximation of fixed points of multifunctions in partial metric spaces

Recently, Reich and Zaslavski [S. Reich and A.J. Zaslavski, Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings, Fixed Point Theory Appl. 2010 (2010), Article ID 518243, 10pages] have studied a new inexact iterative scheme for fixed points ofcontractive multifunctions. In this paper, using the partial Hausdorffmetric introduced by Aydi et al., we prove an analogous to a resultof Reich and Zaslavski for contractive multifunctions in the setting ofpartial metric spaces. An example is given to illustrate our result.&amp;nbsp;

Invariant approximation results in cone metric spaces

‎Some sufficient conditions for the existence of fixed point of mappings‎ ‎satisfying generalized weak contractive conditions is obtained‎. ‎A fixed‎ ‎point theorem for nonexpansive mappings is also obtained‎. ‎As an application‎, ‎some invariant approximation results are derived in cone metric spaces‎.

Common Fixed Points in a Partially Ordered Partial Metric Space

In the first part of this paper, we prove some generalized versions of the result of Matthews in (Matthews, 1994) using different types of conditions in partially ordered partial metric spaces for dominated self-mappings or in partial metric spaces for self-mappings. In the second part, using our results, we deduce a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends the Subrahmanyam characterization of metric completeness.

Common fixed point results on quasi-Banach spaces and integral equations

In this paper we obtain fixed and common fixed point theorems for self-mappings defined on a closed and convex subset C of a quasi-Banach space. We give also a constructive method for finding the common fixed points of the involved mappings. As an application we obtain a result of the existence of solutions of integral equations.

Common fixed points in cone metric spaces

In this paper we consider a notion of g-weak contractive mappings in the setting of cone metric spaces and we give results of common fixed points. This results generalize some common fixed points results in metric spaces and some of the results of Huang and Zhang in cone metric spaces.

Fixed point results for $GP_(Λ,Θ)$-contractive mappings

In this paper, we introduce new notions of GP-metric space and $GP_(Λ,Θ)$-contractive mapping and then prove some fixed point theorems for this class of mappings. Our results extend and generalized Banach contraction principle to GP-metric spaces. An example shows the usefulness of our results.

Fixed points for Geraghty-Contractions in partial metric spaces

We establish some fixed point theorems for mappings satisfying Geraghty-type contractive conditions in the setting of partial metric spaces and ordered partial metric spaces. Presented theorems extend and generalize many existing results in the literature. Examples are given showing that these results are proper extensions of the existing ones. c ©2014 All rights reserved.

Common fixed point results for three maps in G-metric spaces

In this paper, we use the setting of generalized metric spaces to obtain common fixed point results for three maps. These results generalize several well known comparable results in the literature.

Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces

Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004…

Stability of a stochastic SIR system

Abstract We propose a stochastic SIR model with or without distributed time delay and we study the stability of disease-free equilibrium. The numerical simulation of the stochastic SIR model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found.

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.

MR2664252 Aziz, W.; Leiva, H.; Merentes, N.; Sánchez, J. L. Functions of two variables with bounded φ-variation in the sense of Riesz. J. Math. Appl. 32 (2010), 5–23. (Reviewer: Pasquale Vetro)

The authors consider the space $BV_\varphi^R (I^b_a,\mathbb{R})$ of functions $f:I^b_a =[a,b]\times [a,b]\subset \mathbb{R}^2 \to \mathbb{R}$ with a $\varphi$-bounded variation in the sense of Riesz, where $\varphi: [0,+ \infty) \to [0,+ \infty)$ is nondecreasing and continuous with $\varphi(0)=0$ and $\varphi(t) \to +\infty$ as $t \to +\infty$. The authors show that $BV_\varphi^R (I^b_a,\mathbb{R})$ is a Banach algebra. Let $h: I^b_a \times \mathbb{R} \to \mathbb{R}$ and let $H: \mathbb{R}^{I^b_a} \to \mathbb{R}$ be the composition operator associated to $h$, that is the operator defined by $(Hf)(x)= h(x, f(x))$ for each $x \in I^b_a$. Then the authors consider the problem of characterizin…

Fixed points for asymptotic contractions of integral Meir-Keeler type

In this paper we introduce the notion of asymptotic contraction of integral Meir-Keeler type on a metric space and we prove a theorem which ensures existence and uniqueness of fixed points for such contractions. This result generalizes some recent results in the literature.

Common fixed points for α-ψ-φ-contractions in generalized metric spaces

We establish some common fixed point theorems for mappings satisfying an α-ψ-ϕcontractive condition in generalized metric spaces. Presented theorems extend and generalize manyexisting results in the literature.&#x0D; Erratum to “Common fixed points for α-ψ-φ-contractions in generalized metric spaces”&#x0D; In Example 1 of our paper [V. La Rosa, P. Vetro, Common fixed points for α-ψ-ϕcontractions in generalized metric spaces, Nonlinear Anal. Model. Control, 19(1):43–54, 2014] a generalized metric has been assumed. Nevertheless some mistakes have appeared in the statement. The aim of this note is to correct this situation.&#x0D;  

On a pair of fuzzy $\varphi$-contractive mappings

We establish common fixed point theorems for fuzzy mappings under a $\varphi$-contraction condition on a metric space with the d_$\infty$-metric (induced by the Hausdorff metric) on the family of fuzzy sets. The study of fixed points of fuzzy set-valued mappings related to the d_$\infty$-metric is useful in geometric problems arising in high energy physics. Our results generalize some recent results.

MR2944786 Reviewed Turzański, Marian The Bolzano-Poincaré-Miranda theorem—discrete version. Topology Appl. 159 (2012), no. 13, 3130–3135. (Reviewer: Pasquale Vetro) 54H25 (55M20)

The author gives a discrete version of the Bolzano-Poincaré-Miranda theorem. Further, the author uses the main result to prove the Bolzano-Poincaré-Miranda theorem and a theorem on partitions.

Fixed point results on metric and partial metric spaces via simulation functions

We prove existence and uniqueness of fixed point, by using a simulation function and a lower semi-continuous function in the setting of metric space. As consequences of this study, we deduce several related fixed point results, in metric and partial metric spaces. An example is given to support the new theory.

On a stochastic disease model with vaccination

We propose a stochastic disease model where vaccination is included and such that the immunity isn’t permanent. The existence, uniqueness and positivity of the solution and the stability of disease free equilibrium is studied. The numerical simulation is done.

On fixed points of alpha-eta-psi-contractive multifunctions

Recently Samet et al. [B. Samet, C. Vetro, P. Vetro, Fixed point theorem for alpha-psi-contractive type mappings, Nonlinear Anal., 75 (2012), 2154{2165] introduced the notion of alpha-psi-contractive type mappings and established some fixed point theorems in complete metric spaces. Succesively, Asl et al. [J.H. Asl, SH. Rezapour, N. Shahzad, On fixed point of alpha-contractive multifunctions, Fixed Point Theory Appl., 2012, 212 (2012)] introduced the notion of alpha_*-psi-contractive multifunctions and give a fixed point result for these multifunctions. In this paper we obtain certain new fixed point and common fixed point theorems via alpha_*-admissible multifuncions with respect to eta. T…

Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces

Abstract. In this paper, we extend the coupled coincidence point theorems for a mixed g-monotone operator F : X × X → X $F:X\times X\rightarrow X$ obtained by Alotaibi and Alsulami [Fixed Point Theory Appl. (2011), article ID 44], by weakening the involved contractive condition. Two examples are given to illustrate the effectiveness of our generalizations. Our result also generalizes some recent results announced in the literature. Moreover, some applications to integral equations are presented.

Fixed point results for $r$-$(\mathbf{\eta},\xi,\psi)$-contractive mappings of type (I), (II) and (III)

In this paper, we introduce some classes of $r$-$(\eta,\xi,\psi)$-contractive mappings and prove results of fixed point in the setting of complete metric spaces. Some examples and an application to integral equations are given to illustrate the usability of the obtained results.

MR2661185 Reviewed Huang, Xianjiu; Zhu, Chuanxi; Wen, Xi Common fixed point theorem for four non-self-mappings in cone metric spaces. Fixed Point Theory Appl. 2010, Art. ID 983802, 14 pp. (Reviewer: Pasquale Vetro)

Recently, L. G. Huang and X. Zhang [J. Math. Anal. Appl. 332 (2007), no. 2, 1468–1476; MR2324351 (2008d:47111)] defined cone metric spaces by substituting an order normed space for the real numbers and proved some fixed point theorems. In this paper the authors prove a common fixed point theorem for four non-self-mappings in the framework of cone metric spaces. This result is an extension of a common fixed point theorem of Radenović and Rhoades for two non-self-mappings. The paper also contains some illustrative examples. For fixed point results in the framework of cone metric spaces see also [M. Arshad, A. Azam and P. Vetro, Fixed Point Theory Appl. 2009, Art. ID 493965; MR2501489 (2010e:5…

MR3157399 Reviewed: Kesavan, S. Continuous functions that are nowhere differentiable. Math. Newsl. 24 (2013), no. 3, 49–52. (54C05)

The author uses the Baire category theorem to prove the existence of nowhere differentiable functions in C([0,1]). Precisely, the author proves the following: Theorem 1. There exist continuous functions on the interval [0,1] which are nowhere differentiable. In fact, the collection of all such functions forms a dense subset of C([0,1]).

On fixed points of Berinde’s contractive mappings in cone metric spaces

In this paper we establish some common fixed point theorems for two self-mappings satisfying a generalized contractive condition. This result generalizes well known comparable results in the literature. As an application, a necessary and sufficient condition for a fixed point to be a periodic point for the mapping involved therein, without appealing to continuity, in a cone metric space is established.

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.

Some common fixed point results for weakly compatible mappings in cone metric type space

In this paper we consider cone metric type spaces which are introduced as a generalization of symmetric and metric spaces by Khamsi and Hussain in 2010. Then we prove several common fixed point for weakly compatible mappings in cone metric type spaces. All results are proved in the settings of a solid cone, without the assumption of continuity of the mappings.

Fixed points and completeness on partial metric spaces

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of…

MR3136896 Reviewed Ray, S.; Garai, A. The Laplace derivative II. Math. Student 81 (2012), no. 1-4, 177–184. (Reviewer: Pasquale Vetro) 26A24

In a previous paper [Part I, Math. Student 81 (2012), no. 1-4, 171–175; MR3136895], the authors studied some properties of the first-order Laplace derivative. In this paper they study some properties of higher-order Laplace derivatives and give an analogue of Taylor's theorem using higher-order Laplace derivatives.

Fixed point results in cone metric spaces for contractions of Zamfirescu type

We prove a result on points of coincidence and common fixed points in cone metric spaces for two self mappings satisfying a weak generalized contractive condition of Zamfirescu type. We deduce some results on common fixed points for two self mappings satisfying a weak contractive type condition. These results generalize some well-known recent results.

Common Fixed Points of a Pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Dislocated Metric Spaces

Common fixed point results for mappings satisfying locally contractive conditions on a closed ball in an ordered complete dislocated metric space have been established. The notion of dominated mappings is applied to approximate the unique solution of nonlinear functional equations. Our results improve several well-known conventional results.

Fixed point results for $G^m$-Meir-Keeler contractive and $G$-$(\alpha,\psi)$-Meir-Keeler contractive mappings

In this paper, first we introduce the notion of a $G^m$-Meir-Keeler contractive mapping and establish some fixed point theorems for the $G^m$-Meir-Keeler contractive mapping in the setting of $G$-metric spaces. Further, we introduce the notion of a $G_c^m$-Meir-Keeler contractive mapping in the setting of $G$-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a $G$-$(\alpha,\psi)$-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of $G$-metric spaces.

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.

Coupled fixed-point results for T-contractions on cone metric spaces with applications

The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipovićet al. [M. Filipovićet al., “Remarks on “Cone metric spaces and fixed-point theorems of T-Kannan and T-Chatterjea contractive mappings”,” Math. Comput. Modelling 54, 1467–1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain T-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature.

Matematica

On fixed points for a–n–f-contractive multi-valued mappings in partial metric spaces

Recently, Samet et al. introduced the notion of α-ψ-contractive type mappings and established some fixed point theorems in complete metric spaces. Successively, Asl et al. introduced the notion of αӿ-ψ-contractive multi-valued mappings and gave a fixed point result for these multivalued mappings. In this paper, we establish results of fixed point for αӿ-admissible mixed multivalued mappings with respect to a function η and common fixed point for a pair (S; T) of mixed multi-valued mappings, that is, αӿ-admissible with respect to a function η in partial metric spaces. An example is given to illustrate our result.

Common fixed points in cone metric spaces for CJM-pairs

Abstract In this paper we introduce some contractive conditions of Meir–Keeler type for two mappings, called f - M K -pair mappings and f - C J M -pair (from Ciric, Jachymski, and Matkowski) mappings, in the framework of regular cone metric spaces and we prove theorems which guarantee the existence and uniqueness of common fixed points. We give also a fixed point result for a multivalued mapping that satisfies a contractive condition of Meir–Keeler type. These results extend and generalize some recent results from the literature. To conclude the paper, we extend our main result to non-regular cone metric spaces by using the scalarization method of Du.

Fixed point results in cone metric spaces

We prove a result on points of coincidence and common fixed points for three self mappings satisfying a weak generalized contractive type condition in cone metric spaces. We deduce some results on common fixed points for two self mappings satisfying a weak contractive type condition in cone metric spaces. This results generalize some well-known recent results.

Random Stability of an Additive-Quadratic-Quartic Functional Equation

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation f(x+2y)+f(x&#x2212;2y)=2f(x+y)+2f(&#x2212;x&#x2212;y)+2f(x&#x2212;y)+2f(y&#x2212;x)&#x2212;4f(&#x2212;x)&#x2212;2f(x)+f(2y)+f(&#x2212;2y)&#x2212;4f(y)&#x2212;4f(&#x2212;y) in complete random normed spaces.

Common fixed points for self-mappings on partial metric spaces

Abstract In this paper, we prove some results of a common fixed point for two self-mappings on partial metric spaces. Our results generalize some interesting results of Ilić et al. (Appl. Math. Lett. 24:1326-1330, 2011). We conclude with a result of the existence of a fixed point for set-valued mappings in the context of 0-complete partial metric spaces. MSC:54H25, 47H10.

Some fixed point results via R-functions

We establish existence and uniqueness of fixed points for a new class of mappings, by using R-functions and lower semi-continuous functions in the setting of metric spaces. As consequences of this results, we obtain several known fixed point results, in metric and partial metric spaces. An example is given to support the new theory. A homotopy result for operators on a set endowed with a metric is given as application.

PPF dependent fixed point results for triangular $alpha_c$-admissible mappings

We introduce the concept of triangular $alpha_c$-admissible mappings (pair of mappings) with respect to $η_c$ nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular $alpha_c$-admissible mappings (pair of mappings) with respect to $η_c$ nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are also given.

SIRV epidemic model with stochastic perturbation

We propose a stochastic disease model where vaccination is included and such that the immunity is permanent. The existence, uniqueness and positivity of the solution and the stability of the disease free-equilibrium are studied

Fixed point theorems in generalized partially orderedG-metric spaces

In this paper, we consider the concept of a $\Omega$-distance on a complete partially ordered G-metric space and prove some fixed point theorems.

Picard sequence and fixed point results on b -metric spaces

We obtain some fixed point results for single-valued and multivalued mappings in the setting of ab-metric space. These results are generalizations of the analogous ones recently proved by Khojasteh, Abbas, and Costache.

Some Common Fixed Point Results in Cone Metric Spaces

We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.

MR3136189 Reviewed Merghadi, F.; Godet-Thobie, C. Common fixed point theorems under contractive conditions of integral type in symmetric spaces. Demonstratio Math. 46 (2013), no. 4, 757–780. (Reviewer: Pasquale Vetro) 47H10 (47H09)

The problem of establishing the existence of fixed points for mappings satisfying weak contractive conditions in metric spaces has been widely investigated in the last few decades. More recently, many papers have been published extending this study to various metric contexts. In the paper under review, the authors prove some common fixed point results for symmetric (or semi-metric) spaces. They use implicit contractive conditions of integral type for mappings satisfying weak compatibility or occasionally weak compatibility hypotheses. Some examples are given to illustrate the obtained results.

Fixed points for weak $\varphi$-contractions on partial metric spaces

In this paper, following [W.A. Kirk, P.S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003) 79-89], we give a fixed point result for cyclic weak $\varphi$-contractions on partial metric space. A Maia type fixed point theorem for cyclic weak $\varphi$-contractions is also given.

MR2306791

MR2306791

MR2421723 (2009g:54089) 54H25 (47H10) Berinde,Vasile (R-NBM-CS); Pacurar,Madalina Fixed points and continuity of almost contractions. (English summary) Fixed Point Theory 9 (2008), no. 1, 23–34.

recensione

MR2482596 : Babu, G. V. R.; Kameswari, M. V. R. Common fixed point theorems using different contractive type conditions involving rational expressions. Proc. Jangjeon Math. Soc. 11 (2008), no. 2, 113–136.

MR2482596