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: Research Article Iterative Methods for Finding Common Solution of Generalized Equilibrium Problems and Variational Inequality Problems and Fixed Point Problems of a Finite Family of Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 836714 29 pages doi 2010 836714 Research Article Iterative Methods for Finding Common Solution of Generalized Equilibrium Problems and Variational Inequality Problems and Fixed Point Problems of a Finite Family of Nonexpansive Mappings Atid Kangtunyakarn Department of Mathematics Faculty of Science King Mongkut s Institute of Technology Ladkrabang Bangkok 10520 Thailand Correspondence should be addressed to Atid Kangtunyakarn beawrock@ Received 7 October 2010 Accepted 2 November 2010 Academic Editor T. D. Benavides Copyright 2010 Atid Kangtunyakarn. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We introduce a new method for a system of generalized equilibrium problems system of variational inequality problems and fixed point problems by using S-mapping generated by a finite family of nonexpansive mappings and real numbers. Then we prove a strong convergence theorem of the proposed iteration under some control condition. By using our main result we obtain strong convergence theorem for finding a common element of the set of solution of a system of generalized equilibrium problems system of variational inequality problems and the set of common fixed points of a finite family of strictly pseudocontractive mappings. 1. Introduction Let H be a real Hilbert space and let C be a nonempty closed convex subset of H. Let A C H be a nonlinear mapping and let F C X C R be a bifunction. A mapping T of H into itself is called nonexpansive if Tx - Ty x - y for all x y e H. We denote by F T the set of fixed points of T . F T x e H Tx x . Goebel and Kirk 1 showed that F T is always closed convex and also nonempty provided T has a bounded trajectory. A bounded linear operator A on H is called strongly positive
