Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 370197, 25 pages
doi:10.1155/2010/370197
Research Article

A General Iterative Method of Fixed Points for Mixed Equilibrium Problems and Variational Inclusion Problems

Phayap Katchang1 and Poom Kumam1,2

1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, (KMUTT), Bangmod, Bangkok 10140, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 27 October 2009; Accepted 16 March 2010

Academic Editor: Jong Kyukkyungnam Kim

Copyright © 2010 Phayap Katchang 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

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal monotone mappings and inverse-strongly monotone mappings, and the set of fixed points of a family of finitely nonexpansive mappings in the setting of Hilbert spaces. We propose a new iterative scheme for finding the common element of the above three sets. Our results improve and extend the corresponding results of the works by Zhang et al. (2008), Peng et al. (2008), Peng and Yao (2009), as well as Plubtieng and Sriprad (2009) and some well-known results in the literature.