正规结构与不动点定理  

NORMAL STRUCTURE AND FIXED POINT

作　　者：顾文颖[1] 李刚[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2003年第4期4-7,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金(10171087)

摘　　要：设X是具正规结构的Banach空间,C是X中非空弱紧凸子集,T是C上的渐近非扩张型映射,K是T的最小(P)子集,证明了T有不动点的充要条件为K中含T的渐近殆轨道,将不动点定理推广到了k-Lipschitzian半群的情形。Let C be a nonexpansive weakly compact convex subset of a Hanach space X with normal structure, and T:C→C be an asymptotically nonexpansive type mapping. Suppose K be the minimal subset of T with the property (P), then T has a common fixed point if and only if there exists an asymptotic almost-orbit of 7' in K. Futhermore, this paper provides a fixed point theorem for uniformaly k-Lipschitzian semigroup.

关 键 词：巴拿赫空间 k-Lipschitzian半群 正规结构 巴拿赫不动点定理 

分 类 号：O152.7[理学—数学] O177.2[理学—基础数学]