TAILIEUCHUNG - Báo cáo hóa học: "APPROXIMATION COMMON FIXED POINT OF ASYMPTOTICALLY QUASI-NONEXPANSIVE-TYPE MAPPINGS BY THE FINITE STEPS ITERATIVE SEQUENCES"

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: APPROXIMATION COMMON FIXED POINT OF ASYMPTOTICALLY QUASI-NONEXPANSIVE-TYPE MAPPINGS BY THE FINITE STEPS ITERATIVE SEQUENCES | APPROXIMATION COMMON FIXED POINT OF ASYMPTOTICALLY QUASI-NONEXPANSIVE-TYPE MAPPINGS BY THE FINITE STEPS ITERATIVE SEQUENCES JING QUAN SHIH-SEN CHANG AND XIAN JUN LONG Received 26 December 2005 Accepted 11 March 2006 The purpose of this paper is to study sufficient and necessary conditions for finite-step iterative sequences with mean errors for a finite family of asymptotically quasi-nonexpan-sive and type mappings in Banach spaces to converge to a common fixed point. The results presented in this paper improve and extend the recent ones announced by Ghost-Debnath Liu Xu and Noor Chang Shahzad et al. Shahzad and Udomene Chidume et al. and all the others. Copyright 2006 Jing Quan 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 F T D T and N denote the set of fixed points of T the domain of T and the set of positive integers respectively. Definition . Let T D T E - E be a mapping. 1 T is said to be quasi-nonexpansive if F T 0 and II Tx - pH l x - pH for all x G E and p G F T . 2 T is said to be asymptotically nonexpansive if there exists a sequence kn of positive real numbers with kn 1 and iimn. kn 1 such that Tnx - Tny kn x - yll for all x y G E and n G N. 3 T is said to be asymptotically quasi-nonexpansive if F T 0 and there exists a sequence kn of positive real numbers with kn 1 and limn TO kn 1 such that IITnx - pH kn x- pH for all x G E p G F T and all n G N. 4 T is said to be asymptotically nonexpansive type if limsup j sup Tnx - Tny 2 - x- y II2 t 0. n M x yGE Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2006 Article ID 70830 Pages 1-8 DOI FPTA 2006 70830 2 Approximation of common fixed point 5 T is said to be asymptotically quasi-nonexpansive type if .

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