Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 798319, 20 pages
doi:10.1155/2009/798319
Research Article

On Strong Convergence by the Hybrid Method for Equilibrium and Fixed Point Problems for an Inifnite Family of Asymptotically Nonexpansive Mappings

Gang Cai and Chang song Hu

Department of Mathematics, Hubei Normal University, Huangshi 435002, China

Received 17 April 2009; Accepted 9 July 2009

Academic Editor: Tomonari Suzuki

Copyright © 2009 Gang Cai and Chang song Hu. 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 modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space. Then, we prove that such two sequences converge strongly to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of asymptotically nonexpansive mappings. Our results improve and extend the results announced by many others.