Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 601910, 23 pages
doi:10.1155/2011/601910
Research Article

Algorithms of Common Solutions to Generalized Mixed Equilibrium Problems and a System of Quasivariational Inclusions for Two Difference Nonlinear Operators in Banach Spaces

Nawitcha Onjai-uea1,2 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 11 December 2010; Accepted 3 January 2011

Academic Editor: S. Al-Homidan

Copyright © 2011 Nawitcha Onjai-uea 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 consider a new iterative algorithm for finding a common element of the set of generalized mixed equilibrium problems, the set of solutions of a system of quasivariational inclusions for two difference inverse strongly accretive operators, and common set of fixed points for strict pseudo-contraction mappings in Banach spaces. Furthermore, strong convergence theorems of this method were established under suitable assumptions imposed on the algorithm parameters. The results obtained in this paper improve and extend some results in the literature.