Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 719360, 18 pages
doi:10.1155/2009/719360
Research Article

A Hybrid Iterative Scheme for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Banach Spaces

Prasit Cholamjiak

School of Science and Technology, Naresuan University at Phayao, Phayao 56000, Thailand

Received 5 February 2009; Accepted 10 April 2009

Academic Editor: Simeon Reich

Copyright © 2009 Prasit Cholamjiak. 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

The purpose of this paper is to introduce a new hybrid projection algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of the variational inequality for an inverse-strongly monotone operator and the set of fixed points of relatively quasi-nonexpansive mappings in a Banach space. Then we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space.