A Note on Geodesically Bounded R-Trees

被引：0
|
作者：
Kirk, W. A. [1 ]
机构：
[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA
来源：
FIXED POINT THEORY AND APPLICATIONS | 2010年
关键词：
THEOREM;
D O I：
10.1155/2010/393470
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is proved that a complete geodesically bounded R-tree is the closed convex hull of the set of its extreme points. It is also noted that if X is a closed convex geodesically bounded subset of a complete R-tree Gamma, and if a nonexpansive mapping T : X -> Gamma satisfies inf{d (x, T(x)) x is an element of X} = 0, then T has a fixed point. The latter result fails if T is only continuous.
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页数：4
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