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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 538912, 29 pages
http://dx.doi.org/10.1155/2012/538912
Research Article

Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem

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

Received 7 October 2011; Accepted 1 November 2011

Academic Editor: Yeong-Cheng Liou

Copyright © 2012 Tanom Chamnarnpan 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 algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of 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. Furthermore, we give a numerical example which supports our main theorem in the last part.