tailieunhanh - Báo cáo hóa học: " Research Article Weak and Strong Convergence of Multistep Iteration for Finite Family of 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: Research Article Weak and Strong Convergence of Multistep Iteration for Finite Family of Asymptotically Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 31056 15 pages doi 2007 31056 Research Article Weak and Strong Convergence of Multistep Iteration for Finite Family of Asymptotically Nonexpansive Mappings Balwant Singh Thakur and Jong Soo Jung Received 14 March 2007 Accepted 26 May 2007 Recommended by Nan-Jing Huang Strong and weak convergence theorems for multistep iterative scheme with errors for finite family of asymptotically nonexpansive mappings are established in Banach spaces. Our results extend and improve the corresponding results of Chidume and Ali 2007 Cho et al. 2004 Khan and Fukhar-ud-din 2005 Plubtieng et al. 2006 Xu and Noor 2002 and many others. Copyright 2007 B. S. Thakur and J. S. Jung. 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 K be a nonempty subset of a real normed space E. A self-mapping T K - K is said to be nonexpansive if II Tx - Ty II x - y II for all x y in K. T is said to be asymptotically nonexpansive if there exists a sequence rn in 0 oo with limn o. rn 0suchthat ỊỊTnx -TnyỊỊ 1 rn x - y II for all x y in K and n e N. The class of asymptotically nonexpansive mappings which is an important generalization of that of nonexpansive mappings was introduced by Goebel and Kirk 6 . Iteration processes for nonexpansive and asymptotically nonexpansive mappings in Banach spaces including Mann 7 and Ishikawa 8 iteration processes have been studied extensively by many authors to solve the nonlinear operators as well as variational inequalities see 1-22 25 . Noor 13 introduced a three-step iterative scheme and studied the approximate solution of variational inclusion in Hilbert spaces by using the techniques of updating the solution and auxiliary principle. Glowinski and Le Tallec 9 used three-step .

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