tailieunhanh - Báo cáo hóa học: " Research Article A New Iterative Method for Solving Equilibrium Problems and Fixed Point Problems for Infinite Family of Nonexpansive Mappings"

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 A New Iterative Method for Solving Equilibrium Problems and Fixed Point Problems for Infinite Family of Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 165098 18 pages doi 2010 165098 Research Article A New Iterative Method for Solving Equilibrium Problems and Fixed Point Problems for Infinite Family of Nonexpansive Mappings Shenghua Wang 1 Yeol Je Cho 2 and Xiaolong Qin3 1 School of Mathematics and Physics North China Electric Power University Baoding 071003 China 2 Department of Mathematics Education and the RINS Gyeongsang National University Chinju 660-701 Republic of Korea 3 Department of Mathematics Hangzhou Normal University Hangzhou 310036 China Correspondence should be addressed to YeolJe Cho yjcho@ Received 7 January 2010 Revised 21 May 2010 Accepted 11 July 2010 Academic Editor Simeon Reich Copyright 2010 Shenghua Wang 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. We introduce a new iterative scheme for finding a common element of the solutions sets of a finite family of equilibrium problems and fixed points sets of an infinite family of nonexpansive mappings in a Hilbert space. As an application we solve a multiobjective optimization problem using the result of this paper. 1. Introduction Let H be a Hilbert space and C be a nonempty closed and convex subset of H. Let be a bifunction of C X C into R where R is the set of real numbers. The equilibrium problem for the bifunction C X C R is to find x e C such that ỉ x y 0 Vy e C. The set of solutions of the above inequality is denoted by EP G . Many problems arising from physics optimization and economics can reduce to finding a solution of an equilibrium problem. In 2007 S. Takahashi and W. Takahashi 1 first introduced an iterative scheme by the viscosity approximation method for finding a common element of the solutions set of equilibrium problem and the set of fixed points of