Geodesic rays, the “Lion-Man” game, and the fixed point property

Genaro López-Acedo; Adriana Nicolae; Bożena Piątek

doi:10.1016/j.jmaa.2020.123948

Geodesic rays, the “Lion-Man” game, and the fixed point property

Genaro López-Acedo
, Adriana Nicolae
, Bożena Piątek

Department of Mathematics (RMS/RMS1)

University of Seville
Babes-Bolyai University

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

2 Citations (Scopus)

Abstract

This paper focuses on the relation among the existence of different types of curves (such as directional ones, quasi-geodesic or geodesic rays), the (approximate) fixed point property for nonexpansive mappings, and a discrete lion and man game. Our main result holds in the setting of CAT(0) spaces that are additionally Gromov hyperbolic.

Original language	English
Article number	123948
Journal	Journal of Mathematical Analysis and Applications
Volume	487
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2020.123948
Publication status	Published - 1 Jul 2020

Keywords

CAT(0) geometry
Fixed point property
Geodesic ray
Gromov hyperbolicity
Lion and man game

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2020.123948

Cite this

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title = "Geodesic rays, the {\textquotedblleft}Lion-Man{\textquotedblright} game, and the fixed point property",

abstract = "This paper focuses on the relation among the existence of different types of curves (such as directional ones, quasi-geodesic or geodesic rays), the (approximate) fixed point property for nonexpansive mappings, and a discrete lion and man game. Our main result holds in the setting of CAT(0) spaces that are additionally Gromov hyperbolic.",

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AU - Nicolae, Adriana

AU - Piątek, Bożena

PY - 2020/7/1

Y1 - 2020/7/1

N2 - This paper focuses on the relation among the existence of different types of curves (such as directional ones, quasi-geodesic or geodesic rays), the (approximate) fixed point property for nonexpansive mappings, and a discrete lion and man game. Our main result holds in the setting of CAT(0) spaces that are additionally Gromov hyperbolic.

AB - This paper focuses on the relation among the existence of different types of curves (such as directional ones, quasi-geodesic or geodesic rays), the (approximate) fixed point property for nonexpansive mappings, and a discrete lion and man game. Our main result holds in the setting of CAT(0) spaces that are additionally Gromov hyperbolic.

KW - CAT(0) geometry

KW - Fixed point property

KW - Geodesic ray

KW - Gromov hyperbolicity

KW - Lion and man game

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DO - 10.1016/j.jmaa.2020.123948

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Geodesic rays, the “Lion-Man” game, and the fixed point property

Abstract

Keywords

ASJC Scopus subject areas

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