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Báo cáo toán học: " Shrinking projection algorithms for equilibrium problems with a bifunction defined on the dual space of a Banach space"
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Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Shrinking projection algorithms for equilibrium problems with a bifunction defined on the dual space of a Banach space | Chen et al. Fixed Point Theory and Applications 2011 2011 91 http www.fixedpointtheoryandapplications.eom content 2011 1 91 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Shrinking projection algorithms for equilibrium problems with a bifunction defined on the dual space of a Banach space Jia-wei Chen 1 Yeol Je Cho2 and Zhongping Wan1 Correspondence yjcho@gnu.ac.kr 2Department of Mathematics Education and the RINS Gyeongsang National University Chinju 660-701 Republic of Korea Full list of author information is available at the end of the article Abstract Shrinking projection algorithms for finding a solution of an equilibrium problem with a bifunction defined on the dual space of a Banach space in this paper are introduced and studied. Under some suitable assumptions strong and weak convergence results of the shrinking projection algorithms are established respectively. Finally we give an example to illustrate the algorithms proposed in this paper. 2000 Mathematics Subject Classification 47H09 65J15 90C99. Keywords equilibrium problem strong and weak convergence shrinking projection algorithm sunny generalized nonexpansive retraction fixed point 1 Introduction Let o be a nonempty closed subset of a real Hilbert space H. Let g be a bifunction from o X o to R where R is the set of real numbers. The equilibrium problem for g is as follows Find x e Q such that g x y 0 Vy e Q. Many problems in structural analysis optimization management sciences economics variational inequalities and complementary problems coincide to find a solution of the equilibrium problem. Various methods have been proposed to solve some kinds of equilibrium problems in Hilbert and Banach spaces see 1-8 . In 9 Takahashi and Zembayashi proved strong and weak convergence theorems for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in Banach spaces. Ibaraki and Takahashi 10 .