Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 232163, 15 pages
doi:10.1155/2011/232163
Research Article

A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings

Jian-Wen Peng,1 Soon-Yi Wu,2 and Gang-Lun Fan2

1School of Mathematics, Chongqing Normal University, Chongqing 400047, China
2Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan

Received 21 October 2010; Accepted 24 November 2010

Academic Editor: Jen Chih Yao

Copyright © 2011 Jian-Wen Peng et al. 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 scheme based on both hybrid method and extragradient method for finding a common element of the solutions set of a system of equilibrium problems, the fixed points set of a nonexpansive mapping, and the solutions set of a variational inequality problems for a monotone and 𝑘 -Lipschitz continuous mapping in a Hilbert space. Some convergence results for the iterative sequences generated by these processes are obtained. The results in this paper extend and improve some known results in the literature.