Abstract and Applied Analysis
Volume 2011 (2011), Article ID 854360, 19 pages
doi:10.1155/2011/854360
Review Article

The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 23 November 2010; Accepted 27 January 2011

Academic Editor: Ljubisa Kocinac

Copyright © 2011 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 two general hybrid iterative approximation methods (one implicit and one explicit) for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly positive bounded linear operators. Strong convergence theorems of the proposed iterative methods are obtained in a reflexive Banach space which admits a weakly continuous duality mapping. The results presented in this paper improve and extend the corresponding results announced by Marino and Xu (2006), Wangkeeree et al. (in press), and Ceng et al. (2009).