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Research Article A System of Generalized Mixed Equilibrium Problems and Fixed Point Problems for Pseudocontractive Mappings in Hilbert Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 361512 33 pages doi 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 1 Department of Mathematics Faculty of Science King Mongkut s University of Technology Thonburi KMUTT Bangkok 10140 Thailand 2 Department of Mathematics Faculty of Liberal Arts Rajamangala University of Technology Rattanakosin rMuTR Bangkok 10100 Thailand Correspondence should be addressed to Chaichana Jaiboon Received 2 April 2010 Accepted 11 June 2010 Academic Editor A. T. M. Lau Copyright 2010 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 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. 1. Introduction 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. Let S E E be a mapping. In the sequel we will use F S to denote the set of fixed points of S that is F S x e E Sx x .