tailieunhanh - Báo cáo hóa học: " Research Article Convergence Theorems of Fixed Points for a Finite Family of 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 Convergence Theorems of Fixed Points for a Finite Family of Nonexpansive Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 856145 7 pages doi 2008 856145 Research Article Convergence Theorems of Fixed Points for a Finite Family of Nonexpansive Mappings in Banach Spaces Yeol Je Cho 1 Shin Min Kang 2 and Xiaolong Qin2 1 Department of Mathematics and RINS Gyeongsang National University Chinju 660-701 South Korea 2 Department of Mathematics Education and RINS Gyeongsang National University Chinju 660-701 South Korea Correspondence should be addressed to Shin Min Kang smkang@ Received 21 October 2007 Accepted 15 December 2007 Recommended by Jerzy Jezierski We modify the normal Mann iterative process to have strong convergence for a finite family nonex-pansive mappings in the framework of Banach spaces without any commutative assumption. Our results improve the results announced by many others. Copyright 2008 Yeol Je Cho 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 Throughout this paper we assume that E is a real Banach space with the normalized duality mapping J from E into 2E give by J x f E x f x 2 f II x Vx E where E denotes the dual space of E and denotes the generalized duality pairing. We assume that C is a nonempty closed convex subset of E and T C A C a mapping. A point x C 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 C Tx x . Recall that T is nonexpansive if Tx - TyW x - yịị for all x y C. One classical way to study nonexpansive mappings is to use contractions to approximate a nonexpansive mapping see 1 2 . More precisely take t 0 1 and define a contraction Tt C A C by Ttx tu 1 - t Tx Vx C 2 Fixed Point Theory and Applications where u G C is a fixed point. Banach s contraction mapping principle guarantees that Tt .