Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: The shrinking projection method for solving generalized equilibrium problems and common fixed points for asymptotically quasij-nonexpansive mappings | Saewan and Kumam Fixed Point Theory and Applications 2011 2011 9 http content 2011 1 9 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access The shrinking projection method for solving generalized equilibrium problems and common fixed points for asymptotically quasi-j-nonexpansive mappings Siwaporn Saewan and Room Kumam Correspondence poom. kum@ Department of Mathematics Faculty of Science King Mongkut s University of Technology Thonburi Km J T Bangmod Bangkok 10140 Thailand SpringerOpen0 Abstract In this article we introduce a new hybrid projection iterative scheme based on the shrinking projection method for finding a common element of the set of solutions of the generalized mixed equilibrium problems and the set of common fixed points for a pair of asymptotically quasi-j-nonexpansive mappings in Banach spaces and set of variational inequalities for an a-inverse strongly monotone mapping. The results obtained in this article improve and extend the recent ones announced by Matsushita and Takahashi Fixed Point Theory Appl. 2004 1 37-47 2004 Qin et al. Appl. Math. Comput. 215 3874-3883 2010 Chang et al. Nonlinear Anal. 73 22602270 2010 Kamraksa and Wangkeeree J. Nonlinear Anal. Optim. Theory Appl. 1 1 55-69 2010 and many others. AMS Subject Classification 47H05 47H09 47J25 65J15. Keywords Generalized mixed equilibrium problem Asymptotically quasi- j -nonex-pansive mapping Strong convergence theorem Variational inequality Banach spaces 1. Introduction Let E be a Banach space with norm - C be a nonempty closed convex subset of E and let E denote the dual of E. Let f CxC R be a bifunction Ộ C R be a real-valued function and B C E be a mapping. The generalized mixed equilibrium problem is to find x e C such that f x y Bx y x p y p x 0 Vy e C. The set of solutions to is denoted by GMEPf B Q . GMEP f B p x e C f x y Bx y x p y p x 0 Vy e C . If B 0 then the problem reduces into
