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 Viscosity Approximation Methods for Generalized Mixed Equilibrium Problems and Fixed Points of a Sequence of Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 714939 15 pages doi 2008 714939 Research Article Viscosity Approximation Methods for Generalized Mixed Equilibrium Problems and Fixed Points of a Sequence of Nonexpansive Mappings Wei-You Zeng 1 Nan-Jing Huang 1 and Chang-Wen Zhao2 1 Department of Mathematics Sichuan University Chengdu Sichuan 610064 China 2 College of Business and Management Sichuan University Chengdu Sichuan 610064 China Correspondence should be addressed to Nan-Jing Huang nanjinghuang@ Received 17 July 2008 Accepted 11 November 2008 Recommended by Wataru Takahashi We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of common solutions for generalized mixed equilibrium problems and the set of common fixed points of a sequence of nonexpansive mappings in Hilbert spaces. We show a strong convergence theorem under some suitable conditions. Copyright 2008 Wei-You Zeng et al. 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. 1. Introduction Equilibrium problems theory provides us with a unified natural innovative and general framework to study a wide class of problems arising in finance economics network analysis transportation elasticity and optimization which has been extended and generalized in many directions using novel and innovative techniques see 1-8 . Inspired and motivated by the research and activities going in this fascinating area we introduce and consider a new class of equilibrium problems which is known as the generalized mixed equilibrium problems. Let C be a nonempty closed convex subset of a real Hilbert space H and T C 2H a multivalued mapping. Let p C X C R be a real-valued function and H X C X C R an equilibrium-like function that is w u v w v u 0 V w u v e
