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báo cáo hóa học:" Research Article Convergence of Three-Step Iterations Scheme for Nonself Asymptotically 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 Convergence of Three-Step Iterations Scheme for Nonself Asymptotically Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 783178 15 pages doi 10.1155 2010 783178 Research Article Convergence of Three-Step Iterations Scheme for Nonself Asymptotically Nonexpansive Mappings Seyit Temir Department of Mathematics Art and Science Faculty Harran University 63200 Sanliurfa Turkey Correspondence should be addressed to Seyit Temir temirseyit@harran.edu.tr Received 15 February 2010 Revised 2 May 2010 Accepted 30 June 2010 Academic Editor Jerzy Jezierski Copyright 2010 Seyit Temir. 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. Weak and strong convergence theorems of three-step iterations are established for nonself asymptotically nonexpansive mappings in uniformly convex Banach space. The results obtained in this paper extend and improve the recent ones announced by Suantai 2005 Khan and Hussain 2008 Nilsrakoo and Saejung 2006 and many others. 1. Introduction Suppose that X is a real uniformly convex Banach space K is a nonempty closed convex subset of X. Let T be a self-mapping of K. A mapping T is called nonexpansive provided Tx - Ty x - y M for all x y e K. T is called asymptotically nonexpansive mapping if there exists a sequence kn c 1 to with limn .to kn 1 such that Tnx - Tny kn x - y 1.2 for all x y e K and n 1. The class of asymptotically nonexpansive maps which is an important generalization of the class nonexpansive maps was introduced by Goebel and Kirk 1 . They proved that 2 Fixed Point Theory and Applications every asymptotically nonexpansive self-mapping of a nonempty closed convex bounded subset of a uniformly convex Banach space has a fixed point. T is called uniformly L-Lipschitzian if there exists a constant L 0 such that for all x y e K the following inequality holds l Tnx - ryỊỊ L x - y 1.3 for all n 1. Asymptotically .