Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 361512, 33 pages
doi:10.1155/2010/361512
Research Article

A System of Generalized Mixed Equilibrium Problems and Fixed Point Problems for Pseudocontractive Mappings in Hilbert Spaces

Poom Kumam1 and Chaichana Jaiboon2

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

Received 2 April 2010; Accepted 11 June 2010

Academic Editor: A. T. M. Lau

Copyright © 2010 Poom Kumam and Chaichana Jaiboon. 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 analyze a new iterative algorithm for finding a common element of the set of fixed points of strict pseudocontractions, the set of common solutions of a system of generalized mixed equilibrium problems, and the set of common solutions of the variational inequalities with inverse-strongly monotone mappings in Hilbert spaces. Furthermore, we prove new strong convergence theorems for a new iterative algorithm under some mild conditions. Finally, we also apply our results for solving convex feasibility problems in Hilbert spaces. The results obtained in this paper improve and extend the corresponding results announced by Qin and Kang (2010) and the previously known results in this area.