Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 590278, 33 pages
doi:10.1155/2010/590278
Research Article
Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators
1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
3Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
4Department of Finance, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan
5Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan
Received 27 October 2009; Accepted 12 January 2010
Academic Editor: Tomonari Suzuki
Copyright © 2010 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 modified hybrid proximal-point algorithms for finding a common element of the solution set EP of a generalized equilibrium problem and the set T−10∩T˜−10 for two maximal monotone operators T and T˜ defined on a Banach space X. Strong and weak convergence theorems for these two modified hybrid proximal-point algorithms are established.