关于Banach空间中渐近非扩张型半群的不动点的存在性

Abstract

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

CLC Number:

47H09

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

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