Fixed points of locally contractive and nonexpansive set-valued mappings

Approximating fixed points of generalized nonexpansive mappings

On stationary points of nonexpansive set-valued mappings

*Correspondence: [email protected] 1Dpto. de Análisis Matemático, IMUS (Instituto Matemático de la Universidad de Sevilla), Universidad de Sevilla, C/Tarfia s/n, 41012 Sevilla, Spain Full list of author information is available at the end of the article Abstract In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of...

Some Fixed Point Theorems for Nonlinear Set-Valued Contractive Mappings

The Homotopic Invariance for Fixed Points of Set-valued Nonexpansive Mappings*

T h e homotopic invariance of fixed points of set-valued contractions and nonexpansive mappings is studied. As application, nonlinear alternative principles are given. A LeraySchauder alternative and an antipodal theorem for set-valued nonexpansive mappings are also included.

Viscosity Approximation to Common Fixed Points of Families of Nonexpansive Mappings with Weakly Contractive Mappings

Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence x n λ n fx n 1−λ n T n x n , where λ n ∈ 0, 1, {T n } is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence {x n } is proved.