Hybrid shrinking projection method for a generalized equilibrium problem, a maximal monotone operator and a countable family of relatively nonexpansive mappings

Authors:
Lu-Chuan Ceng;Sy-Ming Guu;H. -Y. Hu;Jen-Chih Yao
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China and Scientific Computing Key Laboratory of Shanghai Universities, China;College of Management, Yuan-Ze University, Chung-Li City, Taoyuan Hsien, 33026, Taiwan;Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;Center for General Education, Kaohsiung Medical University, Kaohsiung, 807, Taiwan
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

The purpose of this paper is to introduce and consider a hybrid shrinking projection method for finding a common element of the set EP of solutions of a generalized equilibrium problem, the set @?"n"="0^~F(S"n) of common fixed points of a countable family of relatively nonexpansive mappings {S"n}"n"="0^~ and the set T^-^10 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. It is proven that under appropriate conditions, the sequence generated by the hybrid shrinking projection method, converges strongly to some point in EP@?T^-^10@?(@?"n"="0^~F(S"n)). This new result represents the improvement, complement and development of the previously known ones in the literature.