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 Strong Convergence of a New Iterative Method for Infinite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 392741 24 pages doi 2011 392741 Research Article Strong Convergence of a New Iterative Method for Infinite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces Shenghua Wang1 2 and Baohua Guo1 2 1 National Engineering Laboratory for Biomass Power Generation Equipment North China Electric Power University Baoding 071003 China 2 Department of Mathematics and Physics North China Electric Power University Baoding 071003 China Correspondence should be addressed to Shenghua Wang sheng-huawang@ Received 15 October 2010 Accepted 18 November 2010 Academic Editor Qamrul Hasan Ansari Copyright 2011 S. Wang and B. Guo. 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 an iterative algorithm for finding a common element of the set of solutions of an infinite family of equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space. We prove some strong convergence theorems for the proposed iterative scheme to a fixed point of the family of nonexpansive mappings which is the unique solution of a variational inequality. As an application we use the result of this paper to solve a multiobjective optimization problem. Our result extends and improves the ones of Colao et al. 2008 and some others. 1. Introduction Let H be a real Hilbert space and T be a mapping of H into itself. T is said to be nonexpansive if Tx - Ty x - y Nx y e H. If there exists a point u e H such that Tu u then the point u is called a fixed point of T. The set of fixed points of T is denoted by F T . It is well known that F T is closed convex and also nonempty if T has a bounded trajectory see 1 . 2 Fixed Point Theory and Applications
