Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2012, Article ID 538912, 29 pages doi: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 Tanom Chamnarnpan and Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok 10140, Thailand Correspondence should be addressed to Poom Kumam, poom.kum@kmutt.ac.th Received 7 October 2011; Accepted 1 November 2011 Academic Editor: Yeong-Cheng Liou Copyright q 2012 T. Chamnarnpan and P. 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. 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. 1. Introduction Let C be a closed convex subset of a real Hilbert space H with the inner product 〈·, ·〉 and the norm ‖·‖. Let F be a bifunction of C × C into R, where R is the set of real numbers, ϕ : C →R be a real-valued function. Let Λ be arbitrary index set. The system of mixed equilibrium problem is for finding x ∈ C such that F k ( x, y ) ϕ ( y ) - ϕx ≥ 0, k ∈ Λ, ∀y ∈ C. 1.1 The set of solutions of 1.1 is denoted by SMEPF k , that is, SMEPF k x ∈ C : F k ( x, y ) ϕ ( y ) - ϕx ≥ 0,k ∈ Λ, ∀y ∈ C . 1.2