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Geodesic Ptolemy spaces and fixed points

✍ Scribed by Rafa Espínola; Adriana Nicolae

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 241 KB
Volume: 74
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.08.009

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✦ Synopsis

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.

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