关于Banach空间中渐近非扩张型半群的不动点的存在性

数学物理学报 ›› 2004, Vol. 24 ›› Issue (3): 299-306.

关于Banach空间中渐近非扩张型半群的不动点的存在性

曾六川

上海师范大学数学系上海 200234

出版日期:2004-06-22 发布日期:2004-06-22
基金资助:
高等学校优秀青年教师教学和科研奖励基金、上海市曙光计划基金和上海市教委重点学科经费(部分)资助

On the Existence of Fixed Points for Asymptotically Nonexpansive Type Semigroups in Banach Spaces

ZENG Liu-Chuan

Online:2004-06-22 Published:2004-06-22
Supported by:
高等学校优秀青年教师教学和科研奖励基金、上海市曙光计划基金和上海市教委重点学科经费(部分)资助

摘要/Abstract

摘要：

设C是具有弱一致正规结构的Banach空间X的非空弱紧凸子集, T={T(t):t∈S}是渐近非扩张型半群, 且每个T(t)在C上连续. 该文证明了如下结论:(i) 若X是一致凸的, 则F(T) 非空; (ii) 若T={T(t):t∈S}满足lim inf_{t→∞,t in S}|‖T(t)‖|<+∞, 且在C上弱渐近正则, 则F(T)非空, 其中|‖T(t)‖|是T(t)的精确的Lipsch itz常数,F(T)是T(t),t∈S的所有公共不动点之集.

关键词: 不动点, 渐近非扩张型半群, 弱一致正规结构, 渐近正则性, 渐近中心

Abstract:

Let C be a nonempty weakly compact convex subset of a Banach space X with weak uniform normal structure. Let T={T(t):t∈S} be an asymptotically nonexpansive type semigroup for which each T(t) is continuous on C. It is shown that the following conclusions hold: (i) if X is uniformly convex then F(T) is nonempty; (ii) if T={T(t):t∈S} with liminf_{t→∞,t in S}|‖T(t)‖|<+∞ is weakly asymp totically regular on C then F(T) is nonempty, where |‖T(t)‖| is the exact Lipschitzian constant of T(t), and F(T) is the set of all common fixed points of T(t),t∈S.

Key words: Fixed point, Asymptotically nonexpansive type semigroup, Weak uni form normal structure, Asymptotic regularity, Asymptotic center

中图分类号:

47H09

曾六川. 关于Banach空间中渐近非扩张型半群的不动点的存在性[J]. 数学物理学报, 2004, 24(3): 299-306.

ZENG Liu-Chuan. On the Existence of Fixed Points for Asymptotically Nonexpansive Type Semigroups in Banach Spaces[J]. Acta mathematica scientia,Series A, 2004, 24(3): 299-306.

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