Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 257089, 25 pages
doi:10.1155/2009/257089
Research Article

A New Approximation Scheme Combining the Viscosity Method with Extragradient Method for Mixed Equilibrium Problems

Jian-Wen Peng1 and Soon-Yi Wu2

1College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
2Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan

Received 8 November 2009; Revised 2 December 2009; Accepted 6 December 2009

Academic Editor: Simeon Reich

Copyright © 2009 Jian-Wen Peng and Soon-Yi Wu. 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 approximation scheme combining the viscosity method with extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings and the set of the variational inequality for a monotone, Lipschitz continuous mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend, and improve some well-known results in the literature.