tailieunhanh - Báo cáo hóa học: "IMPLICIT PREDICTOR-CORRECTOR ITERATION PROCESS FOR FINITELY MANY ASYMPTOTICALLY "

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: IMPLICIT PREDICTOR-CORRECTOR ITERATION PROCESS FOR FINITELY MANY ASYMPTOTICALLY | IMPLICIT PREDICTOR-CORRECTOR ITERATION PROCESS FOR FINITELY MANY ASYMPTOTICALLY QUASI- NONEXPANSIVE MAPPINGS L. C. CENG N. C. WONG AND J. C. YAO Received 13 February 2006 Revised 3 June 2006 Accepted 5 June 2006 We study an implicit predictor-corrector iteration process for finitely many asymptotically quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space E. We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case E is a uniformly convex Banach space and the mappings are asymptotically nonexpansive we verify the weak resp. strong convergence of this iteration process to a common fixed point of these mappings if Opial s condition is satisfied resp. one of these mappings is semicompact . Our results improve and extend earlier and recent ones in the literature. Copyright 2006 L. C. Ceng 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 Let E be a real Banach space equipped with norm II II let C be a nonempty subset of E and let T C - C. The set F T x G C Tx x consists of all fixed points of T. Definition . T is said to be 1 nonexpansive if Tx - Ty x- yll Vx y G C 2 asymptotically nonexpansive 3 if there exists a sequence kn TO 1 G 1 to with limn to kn 1 such that Tnx - Tny kn x - yll Vx y G C n 1 3 asymptotically quasi-nonexpansive if F T 0 and there exists a sequence kn TO 1 G 1 to with limn to kn 1 such that Tnx - p kn x- ph Vx G C p G F T n 1 Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2006 Article ID 65983 Pages 1-11 DOI JIA 2006 65983 2 Implicit predictor-corrector iteration process 4 semicompact 9 if for any bounded sequence xn c C with lim -v xn - Txn 0 there exists a strongly .