The fixed point property and unbounded sets in CAT(0) spaces

Rafa Espínola; Bozena Pia̧tek

doi:10.1016/j.jmaa.2013.06.038

The fixed point property and unbounded sets in CAT(0) spaces

Rafa Espínola
, Bozena Pia̧tek

Department of Mathematics (RMS/RMS1)

University of Seville

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

In this work we study the fixed point property for nonexpansive self-mappings defined on convex and closed subsets of a CAT(0) space. We will show that a positive answer to this problem is very much linked with the Euclidean geometry of the space while the answer is more likely to be negative if the space is more hyperbolic. As a consequence we extend a very well known result of W.O. Ray on Hilbert spaces.

Original language	English
Pages (from-to)	638-654
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	408
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2013.06.038
Publication status	Published - 15 Dec 2013

Keywords

Banach-Steinhaus theorem
CAT(0) spaces
Fixed points
Nonexpansive mappings
Unbounded convex sets

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2013.06.038

Cite this

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KW - Banach-Steinhaus theorem

KW - CAT(0) spaces

KW - Fixed points

KW - Nonexpansive mappings

KW - Unbounded convex sets

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ER -

The fixed point property and unbounded sets in CAT(0) spaces

Abstract

Keywords

ASJC Scopus subject areas

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