A Note on Geodesically Bounded -Trees

It is proved that a complete geodesically bounded -tree is the closed convex hull of the set of its extreme points. It is also noted that if is a closed convex geodesically bounded subset of a complete -tree and if a nonexpansive mapping satisfies then has a fixed point. The latter result fails if i...

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Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) 2010-06, Vol.2010 (1)
Main Author: Kirk, WA
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Differential Geometry
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Research Article
Topology
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Summary:It is proved that a complete geodesically bounded -tree is the closed convex hull of the set of its extreme points. It is also noted that if is a closed convex geodesically bounded subset of a complete -tree and if a nonexpansive mapping satisfies then has a fixed point. The latter result fails if is only continuous.
ISSN:1687-1812
DOI:10.1155/2010/393470