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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 287602, 9 pages
http://dx.doi.org/10.1155/2014/287602
Research Article

Two-Step Viscosity Approximation Scheme for Variational Inequality in Banach Spaces

School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China

Received 29 December 2013; Accepted 13 February 2014; Published 24 March 2014

Academic Editor: Adrian Petrusel

Copyright © 2014 Liping Yang and Weiming Kong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper introduces and analyzes a viscosity iterative algorithm for an infinite family of nonexpansive mappings in the framework of a strictly convex and uniformly smooth Banach space. It is shown that the proposed iterative method converges strongly to a common fixed point of , which solves specific variational inequalities. Necessary and sufficient convergence conditions of the iterative algorithm for an infinite family of nonexpansive mappings are given. Results shown in this paper represent an extension and refinement of the previously known results in this area.