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: Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasij-nonexpansive mappings Jong Kyu Kim | Kim Fixed Point Theory and Applications 2011 2011 10 http content 2011 1 10 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-j-nonexpansive mappings Jong Kyu Kim Correspondence jongkyuk@ Department of Mathematics Kyungnam University Masan Kyungnam 631-701 Korea SpringerOpen0 Abstract We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-j-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification 47H05 47H09 47H10 47J25 Keywords Asymptotically quasi-j -nonexpansive mapping Relatively non-expan-sive mapping Generalized projection Equilibrium problem Lower semi-continuous 1. Introduction and Preliminaries Let E be a real Banach space E the dual space of E and C a nonempty closed convex subset of E. Let f be a bifunction from C X C to R where R denotes the set of real numbers. In this paper we consider the following equilibrium problem. Find p e C such that f p y 0 Vy e C. We denote EPf the solution set of the equilibrium problem . That is T f p e C f p y 0 Vy e C . Given a mapping Q C E let f x y Qx y x Vx y e C. Then p e EPf if and only if p is a solution of the following variational inequality problem. Find p such that Qp y p 0 Vy e C. Numerous problems in physics optimization and economics reduce to find a solution of see 1-4 . Let T C C be a mapping. The mapping T is said to be asymptotically regular on C if for any bounded subset K of C 2011 Kim licensee Springer. This is an Open Access article distributed underthe terms ofthe Creative Commons Attribution License .
