Abstract and Applied Analysis
Volume 2009 (2009), Article ID 613524, 22 pages
doi:10.1155/2009/613524
Research Article

Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space

Wariam Chuayjan1 and Sornsak Thianwan2

1Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
2School of Science and Technology, Naresuan Phayao University, Phayao 56000, Thailand

Received 29 May 2009; Accepted 26 August 2009

Academic Editor: Simeon Reich

Copyright © 2009 Wariam Chuayjan and Sornsak Thianwan. 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 and study a new hybrid projection algorithm for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of relatively quasi-nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly-monotone operator in a Banach space. Under suitable assumptions, we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space. The results obtained in this paper extend and improve the several recent results in this area.