摘要
设X为一致凸Banach空间,且其对偶空间X*具Kadec-Klee性质.C为x的非空有界闭凸子集,G是一定向网,{Tt,t∈G)为C上一族渐近非扩张映射.{Ttx0,t∈G)的弱收敛定理为:若x0∈C,使得(a)lim sups∈G lim supt∈G ‖ TsTtx0-Ttx0‖=0,(b)lim sups∈G lim sups∈G‖TsTtx0-TtTsx0‖=0,则存在p∈AF(?),使得Ttx0(?)p0.
Let X be a uniformly convex Banach space such that X* has the Kadec-Klee property. Let C be a closed convex subset of X, G be a directed system and {Tt,t∈G} be asymptotically nonexpansive mappings on C. It is proved in this paper that, if x0∈C satisfies (a) lim sups∈G lim supt∈G ‖ T5Ttx0-Ttx0 ‖=0, (b) lim sups∈G lim supt∈G ‖TsTtx0-TtTsx0 ‖=0, then there exists a p∈AF((?)), such that Txx0(?)p.
出处
《扬州大学学报（自然科学版）》
CAS
CSCD
2004年第4期1-5,共5页
Journal of Yangzhou University：Natural Science Edition
基金
国家自然科学基金资助项目(10171087)
