tailieunhanh - Báo cáo hóa học: " Research Article Browder’s Convergence for Uniformly Asymptotically Regular Nonexpansive Semigroups in Hilbert Spaces"

RTuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: esearch Article Browder’s Convergence for Uniformly Asymptotically Regular Nonexpansive Semigroups in Hilbert Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 418030 8 pages doi 2010 418030 Research Article Browder s Convergence for Uniformly Asymptotically Regular Nonexpansive Semigroups in Hilbert Spaces Genaro Lopez Acedo1 and Tomonari Suzuki2 1 Departamento de Analisis Matematico Facultad de Matematicas Universidad de Sevilla 41080 Sevilla Spain 2 Department of Mathematics Kyushu Institute of Technology Tobata Kitakyushu 804-8550 Japan Correspondence should be addressed to Genaro Lopez Acedo glopez@ Received 6 October 2009 Accepted 14 October 2009 Academic Editor Tomas Dominguez Benavides Copyright 2010 G. Lopez Acedo and T. Suzuki. 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 give a sufficient and necessary condition concerning a Browder s convergence type theorem for uniformly asymptotically regular one-parameter nonexpansive semigroups in Hilbert spaces. 1. Introduction Let C be a closed convex subset of a Hilbert space E. A mapping T on C is called a nonexpansive mapping if Tx - Ty x - y for all x y e C. We denote by F T the set of fixed points of T. Browder see 1 proved that F T is nonempty provided that C is in addition bounded. Kirk in a very celebrated paper see 2 extended this result to the setting of reflexive Banach spaces with normal structure. Browder 3 initiated the investigation of an implicit method for approximating fixed points of nonexpansive self-mappings defined on a Hilbert space. Fix u e C he studied the implicit iterative algorithm Zt tu 1 - i Tzt. Namely zt t e 0 1 is the unique fixed point of the contraction x tu 1 - t Tx x e C. Browder proved that limt 0zt Pu where Pu is the element of F T nearest to u. Extensions to the framework of Banach spaces of Browder s convergence results have been done by many authors including