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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 system of equilibrium problems and asymptotically strict pseudocontractions in the intermediate sense | Duan and Zhao Fixed Point Theory and Applications 2011 2011 13 http www.fixedpointtheoryandapplications.eom content 2011 1 13 RESEARCH Fixed Point Theory and Applications a SpringerOpen Journal Open Access Strong convergence theorems for system of equilibrium problems and asymptotically strict pseudocontractions in the intermediate sense Peichao Duan and Jing Zhao Correspondence pcduancauc@126.com College of Science Civil Aviation University of China Tianjin 300300 PR China Abstract Let Sj Ci be N uniformly continuous asymptotically li-strict pseudocontractions in the intermediate sense defined on a nonempty closed convex subset C of a real Hilbert space H. Consider the problem of finding a common element of the fixed point set of these mappings and the solution set of a system of equilibrium problems by using hybrid method. In this paper we propose new iterative schemes for solving this problem and prove these schemes converge strongly. MSC 47H05 47h09 47H10. Keywords asymptotically strict pseudocontraction in the intermediate sense system of equilibrium problem hybrid method fixed point 1. Introduction Let H be a real Hilbert space and let C be a nonempty closed convex subset of H. A nonlinear mapping S C C is a self mapping of C. We denote the set of fixed points of S by F S i.e. F S x e C Sx x . Recall the following concepts. 1 S is uniformly Lipschitzian if there exists a constant L 0 such that Snx---Sny L x y for all integers n 1 and x y e C. 2 S is nonexpansive if Sx Sy x y for all x y e C. 3 S is asymptotically nonexpansive if there exists a sequence kn of positive numbers satisfying the property lim . . kn 1 and Snx Sny kn x y for all integers n 1 and x y e C. SpringerOpen0 2011 Duan and Zhao licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium provided the original work is
