Nonexpansive Set-valued Mappings Research Articles

Set-valued mappings: fixed point results with $\beta$-function and some applications

Via the so-called $\beta$-function, some fixed-point results for nonexpansive set-valued mappings are obtained. In this study, the results are considered in the context of complete metric spaces which are neither uniformly convex nor compact. Our theorems extend, unify, and improve several recent results in the existing literature. In the end, we apply our new results to ensure the existence of a solution for a nonlinear integral inclusion. Moreover, we approximate the fixed point by a faster iterative process.

Common strongly attractive points of nonexpansive set-valued mappings and applications

Common strongly attractive points of nonexpansive set-valued mappings and applications

Fixed Point and Convergence Results for Nonexpansive Set-Valued Mappings

We present several fixed point and convergence results for nonexpansive set-valued mappings which map a closed subset of a complete metric space into the space.

Porosity results for sets of strict contractions on geodesic metric spaces

We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $\mathrm{CAT}(\kappa)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in these settings. We prove that the strict contractions form a negligible subset of this space in the sense that they form a $\sigma$-porous subset. For separable metric spaces we show that a generic nonexpansive mapping has Lipschitz constant one at typical points of its domain. These results contain the case of nonexpansive self-mappings and the case of nonexpansive set-valued mappings as particular cases.

Fixed point theorems of mean nonexpansive set-valued mappings in Banach spaces

We introduce the concept of a mean nonexpansive set-valued mapping in Banach spaces, and extend Nadler’s fixed point theorem and Lim’s fixed point theorem to the case of mean nonexpansive set-valued mappings. Furthermore, using the characteristic of convexity, Opial property, and (DL)-condition, necessary and sufficient conditions for mean nonexpansive set-valued mappings which have the stationary points in Banach spaces are obtained.

On stationary points of nonexpansive set-valued mappings

AbstractIn this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of such points under certain conditions follows as a consequence of the existence of approximate stationary sequences. In particular we provide abstract extensions of well-known fixed point theorems.

Fixed point sets of set-valued mappings

AbstractWe present new results regarding fixed point sets of various set-valued mappings using the concept of fixed point iteration schemes and the newly defined concept of fixed point resolutions. In particular, we prove that the fixed point sets of certain nonexpansive set-valued mappings are contractible.

FIXED POINT THEOREMS FOR GENERALIZED NONEXPANSIVE SET-VALUED MAPPINGS IN CONE METRIC SPACES

Abstract. In 2007, Huang and Zhang [1] introduced a cone metric spacewith a cone metric generalizing the usual metric space by replacing thereal numbers with Banach space ordered by the cone. They consideredsome xed point theorems for contractive mappings in cone metric spaces.Since then, the xed point theory for mappings in cone metric spaces hasbecome a subject of interest in [1-6] and references therein. In this paper,we consider some xed point theorems for generalized nonexpansive set-valued mappings under suitable conditions in sequentially compact conemetric spaces and complete cone metric spaces. 1. Introduction and PreliminariesIn 2007, Huang and Zhang [1] introduced a cone metric space with a conemetric generalizing the usual metric space by replacing the real numbers withBanach space ordered by the cone. They considered some xed point theoremsfor contractive mappings in cone metric spaces. Since then, the xed pointtheory for mappings in cone metric spaces has become a subject of interest in[1-6] and references therein. Especially, for single-valued mappings, Choudhuryand Metiya [6] considered some xed point theorems for weak contraction incone metric spaces in 2010. In 2011, Wardowski [2] introduced H-cone metricin the collection of subsets of a given cone metric space. And he consideredthe concept of set-valued contraction of Nadler-type and proved a xed pointtheorem for contractive set-valued mappings in H-cone metric spaces. Inspiredand encouraged by the previous works, in this paper we consider some xedpoint theorems for generalized nonexpansive set-valued mappings under suit-able conditions in sequentially compact cone metric spaces and complete conemetric spaces.Let Ebe a real Banach space and Pbe a subset of E.Pis called a cone if and only if

Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings

Taking into account possibly inexact data, we study iterative schemes for approximating fixed points and attractors of contractive and nonexpansive set-valued mappings, respectively. More precisely, we are concerned with the existence of convergent trajectories of nonstationary dynamical systems induced by approximations of a given set-valued mapping.

A Best Approximation Theorem for Nonexpansive Set-Valued Mappings in Hyperconvex Metric Spaces

A Best Approximation Theorem for Nonexpansive Set-Valued Mappings in Hyperconvex Metric Spaces

Generic Existence of Fixed Points for Set-Valued Mappings

We first consider a complete metric space of nonexpansive set-valued mappings acting on a closed convex subset of a Banach space with a nonempty interior, and show that a generic mapping in this space has a fixed point. We then establish analogous results for two complete metric spaces of set-valued mappings with convex graphs.

On Fixed Points of Nonexpansive Set-Valued Mappings

On Fixed Points of Nonexpansive Set-Valued Mappings

On fixed points of nonexpansive set-valued mappings

A theorem is proved concerning the existence of fixed points of nonexpansive set-valued mappings. This generalizes a result of Dotson, Jr. [1].

Fixed points of locally contractive and nonexpansive set-valued mappings

Fixed points of locally contractive and nonexpansive set-valued mappings