Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 572156, 14 pages
doi:10.1155/2011/572156
Research Article

A New Strong Convergence Theorem for Equilibrium Problems and Fixed Point Problems in Banach Spaces

Weerayuth Nilsrakoo

Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand

Received 5 June 2010; Revised 28 December 2010; Accepted 20 January 2011

Academic Editor: Fabio Zanolin

Copyright © 2011 Weerayuth Nilsrakoo. 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 a new iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space. Then, we study the strong convergence of the sequences. With an appropriate setting, we obtain the corresponding results due to Takahashi-Takahashi and Takahashi-Zembayashi. Some of our results are established with weaker assumptions.