Weak and strong convergence theorems for relatively nonexpansive multi-valued mappings in Banach spaces

Simin Homaeipour,Abdolrahman Razani

doi:10.1186/1687-1812-2011-73

Abstract

AbstractIn this paper, an iterative sequence for relatively nonexpansive multi-valued mappings by using the notion of generalized projection is introduced, and then weak and strong convergence theorems are proved.2000 Mathematics Subject Classification: 47H09; 47H10; 47J25.

Highlights

Introduction and preliminaries LetD be a nonempty closed convex subset of a real Banach space X
Where D is a nonempty closed convex subset of a uniformly convex and uniformly smooth Banach space X, ΠD is the generalized projection onto D and {an} is a sequence in [0, 1]
In this article, inspired by Matsushita and Takahashi [10], we introduce the following iterative sequence for finding a fixed point of relatively nonexpansive multi-valued mapping T : D ® N(D)

Summary

Introduction

Introduction and preliminaries LetD be a nonempty closed convex subset of a real Banach space X. [4,9]Let D be a nonempty closed convex subset of a reflexive, strictly convex, and smooth Banach space X.

Results

Conclusion