tailieunhanh - Báo cáo hóa học: " NOTE ON SOME RESULTS FOR ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS AND 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: NOTE ON SOME RESULTS FOR ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS AND ASYMPTOTICALLY NONEXPANSIVE MAPPINGS | NOTE ON SOME RESULTS FOR ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS AND ASYMPTOTICALLY NONEXPANSIVE MAPPINGS YUCHAO TANG AND LIWEI LIU Received 26 May 2006 Revised 5 August 2006 Accepted 13 August 2006 We discuss convergence theorems of modified Ishikawa and Mann iterative sequences with errors for asymptotically pseudocontractive and asymptotically nonexpansive mappings in Banach spaces and the boundedness of the domain and range can be dropped generalizing theorems of Chang. Copyright 2006 Y. Tang and L. Liu. 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 Throughout this paper we assume that E is a real Banach space E is the topological dual space of E is the dual between E and E D T and F T denote the domain of T and the set of all fixed points of T respectively and J E 2E is the normalized duality mapping defined by J x f e E x f x II f II II f II x x e E. Definition . Let T D T c E E be a mapping. 1 T is said to be asymptotically nonexpansive if there exists a sequence kn in 0 to with limn TO kn 1 such that Tnx - Tny kn x- yll for allx y e D T and n 1 2 . 2 T is said to be asymptotically pseudocontractive if there exists a sequence kn in 0 to with limn TO kn 1 and for any x y e D T there exists j x - y e J x - y such that Tnx - Tny j x - y kn x - yll2 for all n 1 2 . Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2006 Article ID 24978 Pages 1-7 DOI FPTA 2006 24978 2 Some results for asymptotically pseudocontractive mappings 3 T is said to be uniformly L-Lipschitzian if there exists L 0 such that Tnx - Tny L x - yll for allx y e D T and n 1 2 . The following proposition follows from Definition immediately. Proposition . 1 If T D T c E E is nonexpansive then T is an asymptocially nonexpansive mapping with a .