tailieunhanh - Báo cáo hóa học: " APPROXIMATING FIXED POINTS OF TOTAL 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: APPROXIMATING FIXED POINTS OF TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS | APPROXIMATING FIXED POINTS OF TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS YA. I. ALBER C. E. CHIDUME AND H. ZEGEYE Received 10 March 2005 Revised 7 August 2005 Accepted 28 August 2005 We introduce a new class of asymptotically nonexpansive mappings and study approximating methods for finding their fixed points. We deal with the Krasnosel skii-Mann-type iterative process. The strong and weak convergence results for self-mappings in normed spaces are presented. We also consider the asymptotically weakly contractive mappings. Copyright 2006 Ya. I. Alber 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 Let K be a nonempty subset of a real linear normed space E. Let T be a self-mapping of K. Then T K K is said to be nonexpansive if Tx - Ty x-yll Vx y e K. T is said to be asymptotically nonexpansive if there exists a sequence kn c 1 to with kn 1 as n to such that for all x y e K the following inequality holds Tnx - Tny kn x- yll Vn 1. The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk 18 as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K then T has a fixed point. Alber and Guerre-Delabriere have studied in 3-5 weakly contractive mappings of the class Cy. Definition . An operator T is called weakly contractive of the class Cy on a closed convex set K of the normed space E if there exists a continuous and increasing function y t defined on R such that y is positive on R 0 y 0 0 limt- TO y t to and Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2006 Article ID 10673 Pages 1-20 DOI FPTA 2006 10673 2 Total asymptotically nonexpansive mappings for all x y e K