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Báo cáo hóa học: "WEAK AND STRONG CONVERGENCE OF FINITE FAMILY WITH ERRORS OF NONEXPANSIVE NONSELF-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: WEAK AND STRONG CONVERGENCE OF FINITE FAMILY WITH ERRORS OF NONEXPANSIVE NONSELF-MAPPINGS | WEAK AND STRONG CONVERGENCE OF FINITE FAMILY WITH ERRORS OF NONEXPANSIVE NONSELF-MAPPINGS S. PLUBTIENG AND K. UNGCHITTRAKOOL Received 27 September 2005 Revised 5 May 2006 Accepted 8 May 2006 We are concerned with the study of a multistep iterative scheme with errors involving a finite family of nonexpansive nonself-mappings. We approximate the common fixed points of a finite family of nonexpansive nonself-mappings by weak and strong convergence of the scheme in a uniformly convex Banach space. Our results extend and improve some recent results Shahzad 2005 and many others. Copyright 2006 S. Plubtieng and K. Ungchittrakool. 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 Let K be a subset of a real normed linear space E and let T be a self-mapping on K. T is said to be nonexpansive provided Tx - Tyll x - yll for all x y e K. Fixed-point iteration process for nonexpansive mappings in Banach spaces including Mann and Ishikawa iteration processes has been studied extensively by many authors to solve the nonlinear operator equations in Hilbert spaces and Banach spaces see 3 7 10 11 15 16 . Tan and Xu 15 introduced and studied a modified Ishikawa process to approximate fixed points of nonexpansive mappings defined on nonempty closed convex bounded subsets of a uniformly convex Banach space E. Five years later Xu 18 introduced iterative schemes known as Mann iterative scheme with errors and Ishikawa iterative scheme with errors. Takahashi and Tamura 14 introduced and studied a generalization of Ishikawa iterative schemes for a pair of nonexpansive mappings in Banach spaces. Recently Khan and Fukhar-ud-din 6 extended their scheme to the modified Ishikawa iterative schemes with errors for two mappings and gave weak and strong convergence theorems. On the other hand iterative techniques for .