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Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 347204,

Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 347204, 30 pages doi:10.1155/2011/347204 Research Article Approximation of Common Solutions to System of Mixed Equilibrium Problems, Variational Inequality Problem, and Strict Pseudo-Contractive Mappings Poom Kumam1, 2 and Chaichana Jaiboon2, 3 1 Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand 2 Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand 3 Department of Mathematics, Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin (RMUTR), Bangkok 10100, Thailand Correspondence should be addressed to Chaichana Jaiboon, chaichana.j@rmutr.ac.th Received 3 October 2010; Accepted 5 March. | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 347204 30 pages doi 10.1155 2011 347204 Research Article Approximation of Common Solutions to System of Mixed Equilibrium Problems Variational Inequality Problem and Strict Pseudo-Contractive Mappings Poom Kumam1 2 and Chaichana Jaiboon2 3 1 Department of Mathematics Faculty of Science King Mongkut s University of Technology Thonburi KMUTT Bangkok 10140 Thailand 2 Centre of Excellence in Mathematics CHE Si Ayuthaya Road Bangkok 10400 Thailand 3 Department of Mathematics Faculty of Liberal Arts Rajamangala University of Technology Rattanakosin RMUTR Bangkok 10100 Thailand Correspondence should be addressed to Chaichana Jaiboon chaichana.j@rmutr.ac.th Received 3 October 2010 Accepted 5 March 2011 Academic Editor Jong Kim Copyright 2011 P. Kumam and C. 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. We introduce an iterative algorithm for finding a common element of the set of fixed points of strict pseudocontractions mapping the set of common solutions of a system of two mixed equilibrium problems and the set of common solutions of the variational inequalities with inverse strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. Finally we apply our results for solving convex feasibility problems in Hilbert spaces. Our results improve and extend the corresponding results announced by many others recently. 1. Introduction Throughout this paper we denote by N and R the sets of positive integers and real numbers respectively. Let H be a real Hilbert space with inner product and norm II-II and let E be a nonempty closed convex subset of H. We denote weak convergence and strong convergence by notations and respectively. Recall that a mapping f E E is an .