关于Banach空间中渐近非扩张型半群的不动点的存在性

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.

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

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.