tailieunhanh - Báo cáo hóa học: "Research Article Strong Convergence Theorems for Countable Lipschitzian Mappings and Its Applications in Equilibrium and Optimization Problems"

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 Theorems for Countable Lipschitzian Mappings and Its Applications in Equilibrium and Optimization Problems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 462489 12 pages doi 2009 462489 Research Article Strong Convergence Theorems for Countable Lipschitzian Mappings and Its Applications in Equilibrium and Optimization Problems Liping Yang1 and Yongfu Su2 1 Department of Fundamental Tianjin Institute of Urban Construction Tianjin 300384 China 2 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China Correspondence should be addressed to Yongfu Su suyongfu@ Received 21 October 2008 Revised 20 December 2008 Accepted 5 March 2009 Recommended by Naseer Shahzad The purpose of this paper is to propose a modified hybrid method in mathematical programming and to obtain some strong convergence theorems for common fixed points of a countable family of Lipschitzian mappings. Further we apply our results to solve the equilibrium and optimization problems. The results of this paper improved and extended the results of W. Nilsrakoo and S. Saejung 2008 and some others in some respects. Copyright 2009 L. Yang and Y. Su. 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 and Preliminaries Let H be a real Hilbert space with inner product and norm II II and let C be a nonempty subset of H. A mapping T C C is said to be Lipschitzian if there exists a positive constant L such that Tx - Ty L x - yll Vx y e C. In this case T is also said to be L-Lipschitzian. Throughout the paper we assume that every Lipschitzian mapping is L-Lipschitzian with L 1. If L 1 then T is known as a nonexpansive mapping. We denote by F T the set of fixed points of T. There are many methods for approximating the fixed points of a nonexpansive mapping. In 1953 Mann 1 introduced the following iteration method xn 1 anxn 1 an Txn 1 2 2 Fixed Point Theory and .