Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 590278, 33 pages
doi:10.1155/2010/590278
Strong and weak convergence theorems for common solutions of generalized equilibrium problems and zeros of maximal monotone operators
L.-C. Zeng1
, Q.H. Ansari2
, David S. Shyu3
and J.-C. Yao4
1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
3Department of Finance, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan
4Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan
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.