Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 943275, 25 pages
doi:10.1155/2010/943275
Research Article

Some Iterative Methods for Solving Equilibrium Problems and Optimization Problems

Huimin He,1 Sanyang Liu,1 and Qinwei Fan2

1Department of Mathematics, Xidian University, Xi'An 710071, China
2Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China

Received 3 September 2010; Accepted 29 October 2010

Academic Editor: Vijay Gupta

Copyright © 2010 Huimin He 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 for finding a common element of the set of solutions of the equilibrium problems, the set of solutions of variational inequality for a relaxed cocoercive mapping, and the set of fixed points of a nonexpansive mapping. The results presented in this paper extend and improve some recent results of Ceng and Yao (2008), Yao (2007), S. Takahashi and W. Takahashi (2007), Marino and Xu (2006), Iiduka and Takahashi (2005), Su et al. (2008), and many others.