tailieunhanh - Báo cáo hóa học: " Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications"

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 for equilibrium problems and fixed point problems: A new iterative method, some comments and applications | He and Du Fixed Point Theory and Applications 2011 2011 33 http content 2011 1 33 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Strong convergence theorems for equilibrium problems and fixed point problems A new iterative method some comments and applications Zhenhua He 1 II and Wei-Shih Du2 Correspondence wsdu@nknucc. 2Department of Mathematics National Kaohsiung Normal University Kaohsiung 824 Taiwan Full list of author information is available at the end of the article Springer Abstract In this paper we introduce a new approach method to find a common element in the intersection of the set of the solutions of a finite family of equilibrium problems and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Under appropriate conditions some strong convergence theorems are established. The results obtained in this paper are new and a few examples illustrating these results are given. Finally we point out that some so-called mixed equilibrium problems and generalized equilibrium problems in the literature are still usual equilibrium problems. 2010 Mathematics Subject Classification 47H09 47H10 47J25. Keywords strong convergence iterative method equilibrium problem fixed point problem 1 Introduction and preliminaries Throughout this paper we assume that H is a real Hilbert space with zero vector 0 whose inner product and norm are denoted by Ộ Ộ and respectively. The symbols N and R are used to denote the sets of positive integers and real numbers respectively. Let K be a nonempty closed convex subset of H and T K H be a mapping. In this paper the set of fixed points of T is denoted by F T . We use symbols and to denote strong and weak convergence respectively. For each point x e H there exists a unique nearest point in K denoted by PKx such that II x - Pkx II II x - y II V y e K. The mapping PK is called the metric projection from H onto K. It is well known that