tailieunhanh - Báo cáo hóa học: " Research Article An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach 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 An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 350483 10 pages doi 2008 350483 Research Article An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces Shenghua Wang Lanxiang Yu and Baohua Guo School of Mathematics and Physics North China Electric Power University Baoding 071003 China Correspondence should be addressed to Shenghua Wang sheng-huawang@ Received 6 May 2008 Accepted 24 August 2008 Recommended by William Kirk Let K be a nonempty closed convex subset of a reflexive Banach space E with a weakly continuous dual mapping and let Ti TO1 be an infinite countable family of asymptotically nonexpansive mappings with the sequence kin satisfying kin 1 for each i 1 2 . n 1 2 . and limn TOkjn 1 for each i 1 2 . In this paper we introduce a new implicit iterative scheme generated by Ti TO1 and prove that the scheme converges strongly to a common fixed point of Tj TO1 which solves some certain variational inequality. Copyright 2008 Shenghua Wang et al. 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 E be a Banach space and let K be a nonempty closed convex subset of E. Let T K K be a mapping. Then T is called nonexpansive if Tx - Ty x - yll L1 for all x y e K. T is called asymptotically nonexpansive if there exists a sequence kn c 1 to that converges to 1 as n TO such that Tnx - Tny kn x - y for all x y e K and all n 1. Obviously a nonexpansive mapping is asymptotically nonexpansive. In 1 Goebel and Kirk originally introduced the concept of asymptotically nonexpansive mappings and proved that if E is a uniformly convex Banach space and K is a nonempty closed convex bounded subset of E then every asymptotically nonexpansive 2 Fixed Point Theory .