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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 695183, 20 pages
http://dx.doi.org/10.1155/2012/695183
Research Article

The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces

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

Received 5 August 2012; Accepted 12 December 2012

Academic Editor: Abdelaziz Rhandi

Copyright © 2012 Rabian Wangkeeree and Pakkapon Preechasilp. 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 the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.