tailieunhanh - Báo cáo hóa học: " Research Article Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex 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 Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 150539 9 pages doi 2010 150539 Research Article Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces Liang-Gen Hu 1 Wei-Wei Lin 2 and Jin-Ping Wang1 1 Department of Mathematics Ningbo University Zhejiang 315211 China 2 School of Computer Science and Engineering South China University of Technology Guangzhou 510640 China Correspondence should be addressed to Liang-Gen Hu hulianggen@ Received 20 April 2010 Accepted 26 August 2010 Academic Editor W. Takahashi Copyright 2010 Liang-Gen Hu 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. The viscosity approximation methods are employed to establish strong convergence theorems of the modified Mann iteration scheme to A-strict pseudocontractions in p-uniformly convex Banach spaces with a uniformly Gateaux differentiable norm. The main result improves and extends many nice results existing in the current literature. 1. Introduction Let E be a real Banach space and let C be a nonempty closed convex subset E. We denote by J the normalized duality map from E to 2E defined by Jx A p E x 2 X 2 p e1. J x x 3 x x x x x 3 . . A mapping T C C is said to be a l-strictly pseudocontractive mapping see . 1 if there exists a constant 0 A 1 such that Tx - TyW2 IIx - y II2 All I - T x - I - T y 2 2 Fixed Point Theory and Applications for all x y e C. We note that the class of T-strict pseudocontractions strictly includes the class of nonexpansive mappings which are mapping T on C such that Tx - Ty x - yịị for all x y e C. Obviously T is nonexpansive if and only if T is a 0-strict pseudocontraction. A mapping T C C is said to be a T-strictly pseudocontractive mapping with respect to p if for all x y e C there