Search results for "Fixed points"
showing 9 items of 29 documents
Common fixed points for self mappings on compact metric spaces
2013
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.
Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space
2020
This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains …
MR2670689 Rezapour, Shahram; Khandani, Hassan; Vaezpour, Seyyed M. Efficacy of cones on topological vector spaces and application to common fixed poi…
2011
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…
MR2684111 Kadelburg, Zoran; Radenović, Stojan; Rakočević, Vladimir Topological vector space-valued cone metric spaces and fixed point theorems. Fixed…
2011
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…
PPF dependent fixed point results for triangular $alpha_c$-admissible mappings
2014
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.
Fixed points for weak $\varphi$-contractions on partial metric spaces
2011
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.
On fixed points of alpha-eta-psi-contractive multifunctions
2014
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…
Wardowski conditions to the coincidence problem
2015
In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find p ∈ X such that Tp = Sp, where X is a nonempty set, Y is a complete metric space, and T, S:X → Y are two mappings satisfying a Wardowski type condition of contractivity. Later on, we will state the convergence of the Picard-Juncgk iteration process to the above coincidence problem as well as a rate of convergence for this iteration scheme. Finally, we shall apply our results to study the existence and uniqueness of a solution as well as the convergence of the Picard-Juncgk iteration process toward the solution of a second order differential equation. Ministerio de Economía y Competi…
Fixed point results for α-implicit contractions with application to integral equations
2016
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.