Abstract and Applied Analysis
Volume 2010 (2010), Article ID 763207, 12 pages
doi:10.1155/2010/763207
Research Article

Mixed Approximation for Nonexpansive Mappings in Banach Spaces

Qing-Bang Zhang,1 Fu-Quan Xia,2 and Ming-Jie Liu1

1College of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China
2Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610064, China

Received 14 November 2009; Accepted 20 January 2010

Academic Editor: Jean Pierre Gossez

Copyright © 2010 Qing-Bang Zhang et al. 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

The mixed viscosity approximation is proposed for finding fixed points of nonexpansive mappings, and the strong convergence of the scheme to a fixed point of the nonexpansive mapping is proved in a real Banach space with uniformly Gâteaux differentiable norm. The theorem about Halpern type approximation for nonexpansive mappings is shown also. Our theorems extend and improve the correspondingly results shown recently.