International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 619813, 25 pages
doi:10.1155/2011/619813
Research Article

A General Iterative Algorithm for Generalized Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok 10140, Thailand

Received 1 December 2010; Revised 28 January 2011; Accepted 17 February 2011

Academic Editor: Vittorio Colao

Copyright © 2011 Thanyarat Jitpeera and Poom Kumam. 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 general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Marino and Xu (2006), Su et al. (2008), Klin-eam and Suantai (2009), Tan and Chang (2011), and some other authors.