Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 728028, 43 pages
doi:10.1155/2010/728028
Research Article

Strong Convergence for Generalized Equilibrium Problems, Fixed Point Problems and Relaxed Cocoercive Variational Inequalities

Chaichana Jaiboon1,2 and Poom Kumam1

1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, KMUTT, Bangkok 10140, Thailand
2Department of Mathematics, Faculty of Applied Liberal Arts, Rajamangala University of Technology, Rattanakosin, RMUTR, Bangkok 10100, Thailand

Received 31 October 2009; Accepted 1 February 2010

Academic Editor: Jong Kim

Copyright © 2010 Chaichana Jaiboon 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 iterative scheme for finding the common element of the set of solutions of the generalized equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of the variational inequality problems for a relaxed (u,v)-cocoercive and ξ-Lipschitz continuous mapping in a real Hilbert space. Then, we prove the strong convergence of a common element of the above three sets under some suitable conditions. Our result can be considered as an improvement and refinement of the previously known results.