Geodesic Ptolemy spaces and fixed points

In this paper we study the regularity of geodesic Ptolemy spaces and apply our findings to metric fixed point theory. It is an open question whether such spaces with a continuous midpoint map are CAT(0) spaces. We prove that if a certain uniform continuity is imposed on such a midpoint map then thes...

Full description

Saved in:
Bibliographic Details
Published inNonlinear analysis Vol. 74; no. 1; pp. 27 - 34
Main Authors Espínola, Rafa, Nicolae, Adriana
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Ltd 2011
Elsevier
Subjects
CAT
Differential geometry
Exact sciences and technology
Fixed point
Geodesic space
Geometry
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Nonexpansive mapping
Ptolemy inequality
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Geodesic space
Ptolemy inequality
Nonexpansive mapping
CAT
Fixed point
Fix point
Nonlinear analysis
Geodesic
Mathematical model
Fixed point space
Online AccessGet full text

Cover

More Information
Summary:In this paper we study the regularity of geodesic Ptolemy spaces and apply our findings to metric fixed point theory. It is an open question whether such spaces with a continuous midpoint map are CAT(0) spaces. We prove that if a certain uniform continuity is imposed on such a midpoint map then these spaces, if complete, are reflexive (that is, the intersection of decreasing families of bounded closed and convex subsets is nonempty) and that bounded sequences have unique asymptotic centers. These properties will then be applied to yield a series of fixed point results specific to CAT(0) spaces.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2010.08.009