Strong convergence for solving a general system of variational inequalities and fixed point problems in Banach spaces

Lu-Chuan Ceng,Nawab Hussain,Abdul Latif,Jen-Chih Yao

doi:10.1186/1029-242x-2013-334

Abstract

Abstract In this paper, we propose and analyze some iterative algorithms by hybrid viscosity approximation methods for solving a general system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a uniformly convex Banach space which has a uniformly Gâteaux differentiable norm, and we prove some strong convergence theorems under appropriate conditions. The results presented in this paper improve, extend, supplement and develop the corresponding results recently obtained in the literature. MSC:49J30, 47H09, 47J20.

Highlights

Let X be a real Banach space whose dual space is denoted by X∗
T exists for all x, y ∈ U; in this case, X is said to have a Gâteaux differentiable norm
It is said to be uniformly smooth if this limit is attained uniformly for x, y ∈ U

Summary

Introduction

Let X be a real Banach space whose dual space is denoted by X∗. Let U = {x ∈ X : x = } denote the unit sphere of X. ) and a common fixed point problem of an infinite family of nonexpansive mappings in a uniformly convex and -uniformly smooth Banach space. ) and the set of common fixed points of an infinite family of nonexpansive mappings in a real uniformly convex Banach space which has a uniformly Gâteaux differentiable norm.

Results

Conclusion