Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 671754, 24 pages
doi:10.1155/2011/671754
Research Article

New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces

Kamonrat Nammanee1,2 and Rabian Wangkeeree2,3

1Department of Mathematics, School of Science and Technology, Phayao University, Phayao 56000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 5 October 2010; Accepted 13 November 2010

Academic Editor: Qamrul Hasan Ansari

Copyright © 2011 Kamonrat Nammanee and Rabian Wangkeeree. 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

We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Finally, we apply our results to solve the the equilibrium problems and the problem of finding a zero of an accretive operator. The results presented in this paper mainly improve on the corresponding results reported by many others.