tailieunhanh - Báo cáo hóa học: " Research Article Convergence of Iterative Sequences for Common Zero Points of a Family of m-Accretive 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 Convergence of Iterative Sequences for Common Zero Points of a Family of m-Accretive Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 216173 12 pages doi 2011 216173 Research Article Convergence of Iterative Sequences for Common Zero Points of a Family of m-Accretive Mappings in Banach Spaces Yuan Qing 1 Sun Young Cho 2 and Xiaolong Qin1 1 Department of Mathematics Hangzhou Normal University Hangzhou 310036 China 2 Department of Mathematics Gyeongsang National University Jinju 660-701 Republic of Korea Correspondence should be addressed to Sun Young Cho ooly61@ Received 21 November 2010 Accepted 8 February 2011 Academic Editor Yeol J. Cho Copyright 2011 Yuan Qing 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. We introduce implicit and explicit viscosity iterative algorithms for a finite family of m-accretive operators. Strong convergence theorems of the iterative algorithms are established in a reflexive Banach space which has a weakly continuous duality map. 1. Introduction Let E be a real Banach space and let J denote the normalized duality mapping from E into 2E given by J x f e E x f x 2 f II2 x e E where E denotes the dual space of E and denotes the generalized duality pairing. In the sequel we denote a single-valued normalized duality mapping by j. Let K be a nonempty subset of E. Recall that a mapping f K K is said to be a contraction if there exists a constant a e 0 1 such that Ilf x - f y allx-yib Nx y e K- Recall that a mapping T K K is said to be nonexpansive if Tx - Tytf Hx - y Nx y e K. 2 Fixed Point Theory and Applications A point x e K is a fixed point of T provided Tx x. Denote by F T the set of fixed points of T that is F T x e K Tx x . Given a real number t e 0 1 and a contraction f C C we define a mapping Tfx tf x 1 - tỴTx x e K. It is obviously that Tf is a contraction on K. In fact for