Journal of Applied Mathematics
Volume 2012 (2012), Article ID 572326, 18 pages
http://dx.doi.org/10.1155/2012/572326
Research Article

Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings

Qiao-Li Dong,1 Yan-Ni Guo,1 and Fang Su2

1College of Science, Civil Aviation University of China, Tianjin 300300, China
2College of Science, National University of Defense Technology, Changsha 410073, China

Received 29 November 2011; Accepted 5 December 2011

Academic Editor: Yonghong Yao

Copyright © 2012 Qiao-Li Dong 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

Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove the strong convergence theorem of the studied iterative method. The results of this paper extend and improve the results of Ceng et al., (2008), W. Kumam and P. Kumam, (2009), Yao et al., (2010) and many others.