tailieunhanh - Báo cáo hóa học: " Research Article Convergence Theorems of Three-Step Iterative Scheme for a Finite Family of Uniformly Quasi-Lipschitzian Mappings in Convex Metric Spaces"

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 Convergence Theorems of Three-Step Iterative Scheme for a Finite Family of Uniformly Quasi-Lipschitzian Mappings in Convex Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 891965 12 pages doi 2009 891965 Research Article Convergence Theorems of Three-Step Iterative Scheme for a Finite Family of Uniformly Quasi-Lipschitzian Mappings in Convex Metric Spaces Tian You-xian and Yang Chun-de Institute of Applied Mathematics Chongqing University of Posts and Telecommunications Chongqing 400065 China Correspondence should be addressed to Tian You-xian tianyx@ Received 9 December 2008 Accepted 25 March 2009 Recommended by Nanjing Huang We consider a new Noor-type iterative procedure with errors for approximating the common fixed point of a finite family of uniformly quasi-Lipschitzian mappings in convex metric spaces. Under appropriate conditions some convergence theorems are proved for such iterative sequences involving a finite family of uniformly quasi-Lipschitzian mappings. The results presented in this paper extend improve and unify some main results in previous work. Copyright 2009 T. You-xian and Y. Chun-de. 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 Takahashi 1 introduced a notion of convex metric spaces and studied the fixed point theory for nonexpansive mappings in such setting. For the convex metric spaces Kirk 2 and Goebel and Kirk 3 used the term hyperbolic type space when they studied the iteration processes for nonexpansive mappings in the abstract framework. For the Banach space Petryshyn and Williamson 4 proved a sufficient and necessary condition for Picard iterative sequences and Mann iterative sequence to converge to fixed points for quasi-nonexpansive mappings. In 1997 Ghosh and Debnath 5 extended the results of 4 and gave the sufficient and necessary condition for Ishikawa iterative sequence to converge to fixed .