Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 780764, 15 pages
doi:10.1155/2011/780764
Research Article

An Iteration Method for Common Solution of a System of Equilibrium Problems in Hilbert Spaces

Jong Kyu Kim1 and Nguyen Buong2

1Department of Mathematics Education, Kyungnam University, Masan Kyunganm 631-701, Republic of Korea
2Department of Mathematics, Vietnamse Academy of Science and Technology, Institute of Information Technology, 18, Hoang Quoc Viet, q. Cau Giay, Hanoi 122100, Vietnam

Received 11 December 2010; Revised 3 March 2011; Accepted 4 March 2011

Academic Editor: Qamrul Hasan Ansari

Copyright © 2011 Jong Kyu Kim and Nguyen Buong. 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

The strong convergence theorem is proved for finding a common solution for a system of equilibrium problems: find 𝑢 ∗ ∈ 𝑆 ∶ = ∩ 𝑁 𝑖 = 1 E P ( 𝐹 𝑖 ) , E P ( 𝐹 𝑖 ) ∶ = { 𝑧 ∈ 𝐶 ∶ 𝐹 𝑖 ( 𝑧 , 𝑣 ) ≥ 0 ∀ 𝑣 ∈ 𝐶 } , 𝑖 = 1 , … , 𝑁 , where 𝐶 is a closed convex subset of a Hilbert space 𝐻 and 𝐹 𝑖 are 𝑁 bifunctions from 𝐶 × 𝐶 into R given exactly or approximatively. As an application, finding a common solution for a system of variational inequality problems is given.