Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 751383, 7 pages
doi:10.1155/2008/751383
Research Article

Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces

Jing Zhao,1 Songnian He,1 and Yongfu Su2

1College of Science, Civil Aviation University of China, Tianjin 300300, China
2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Received 25 August 2007; Accepted 16 December 2007

Academic Editor: Tomonari Suzuki

Copyright © 2008 Jing Zhao 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 purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping T and a finite family of nonexpansive mappings {Ti}i=1N, respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.