Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 720371, 15 pages
Research Article

Common Solutions of an Iterative Scheme for Variational Inclusions, Equilibrium Problems, and Fixed Point Problems

Jian-Wen Peng,1 Yan Wang,1 David S. Shyu,2 and Jen-Chih Yao3

1College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
2Department of Finance, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan
3Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan

Received 24 October 2008; Accepted 6 December 2008

Academic Editor: Ram U. Verma

Copyright © 2008 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.


We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings, the set of solutions of an equilibrium problem, and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. The results in this paper unify, extend, and improve some well-known results in the literature.