[PDF] Top 20 An approximation method for common fixed points of a finite family of asymptotic pointwise nonexpansive mappings

... fixed points of a certain ...fixed points exist, but also to be able to construct that fixed ...the approximation of fixed points for various types of mappings (see, ... See full document

... the nonexpansive retraction of X onto C, T : C → X a given ...be nonexpansive if kT x − T yk ≤ kx − yk for all x, y ∈ C. The fixed point set of T denoted by F (T ) such that F (T ) = {x ∈ C : x = T ... See full document

... In this section, we prove strong convergence of an iterative sequence generated by the hybrid method in mathematical programming. We start with the following useful common tools. Lemma 3.1. Let C be a ... See full document

... iteration method based on the steepest descent method and Krasnoselskii-Mann type method for finding a solution of a variational inequality involving a Lipschitz continuous and strongly monotone ... See full document

... a common element in the set of common fixed points of a finite family of quasi-φ-nonexpansive mappings, the set of common solutions of a finite ... See full document

... Recall that a point x ¯ ∈ K is said to be a fixed point of T if T(¯ x) = x. We denote the set of ¯ fixed points of T by F(T ), i.e., F(T ) := {¯ x ∈ K : T x ¯ = x}. Therefore, finding a solution to ¯ the split ... See full document

... on common fixed points for a family of commuting asymptotic pointwise nonexpansive ...of fixed points for multivalued mappings happens under very weak ... See full document

... iterative method for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of a ... See full document

... for approximation of common fixed points of a finite family of non- expansive mappings ...asymptotically nonexpansive mappings for which Tx − T y ≤ x − y ∀ ... See full document

... the asymptotic regularity of T at a point x can be weakened to the so-called weakly asymptotic regularity of T at x, defined as follows: T is weakly asymptotic regular at x ∈ K ... See full document

... of common fixed points for a finite family of nonexpansive mappings has been considered by many authors see 1–4 and the references ...the fixed point sets of a ... See full document

... Motivated and inspired by the above research work of Zeng and Yao [13] and Wang [14], in this paper, we will propose a new explicit iteration scheme with perturbed map- ping for approximation of common ... See full document

... Main Results In this section, we prove weak and strong convergence theorems of the iterative scheme 1.1 for a finite family of nonexpansive mappings in a uniformly convex Banach space.. [r] ... See full document

... two points of X are joined by a rectifiable path (that is, a path of finite length) and the distance between any two points of X is taken to be the infimum of the lengths of all recti- fiable paths ... See full document

... Let E be a reflexive Banach space with a uniformly Gˆateaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a ... See full document

... typical method of proof for the fixed point theorems in Banach and metric spaces is to construct a fixed point by finding an element on which a specific type function attains its ...this method, one has to know ... See full document

... a finite family of nonexpansive ...the common fixed points of a finite family of nonexpansive nonself-mappings by weak and strong conver- gence of the ... See full document

... descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility and Optimization and ... See full document

... sunny nonexpansive retract of C if there exists a sunny nonexpansive retraction of C onto ...sunny nonexpansive retraction from C onto ...and nonexpansive if and only if there holds the ... See full document

... In this paper, we will study the strong convergence of the generalized Mann-type iteration scheme see Definition 2.1 for hemicontractive and, respectively, pseudocontractive mappings. As we will see, our theorems ... See full document