Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 896252, 34 pages
doi:10.1155/2009/896252
Research Article

Iterative Schemes for Generalized Equilibrium Problem and Two Maximal Monotone Operators

L. C. Zeng,1,2 Y. C. Lin,3 and J. C. Yao4

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Science Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
3Department of Occupational Safety and Health, China Medical University, Taichung 404, Taiwan
4Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan

Received 20 July 2009; Accepted 27 October 2009

Academic Editor: Yeol Je Cho

Copyright © 2009 L. C. Zeng 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

The purpose of this paper is to introduce and study two new hybrid proximal-point algorithms for finding a common element of the set of solutions to a generalized equilibrium problem and the sets of zeros of two maximal monotone operators in a uniformly smooth and uniformly convex Banach space. We established strong and weak convergence theorems for these two modified hybrid proximal-point algorithms, respectively.