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

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...

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Detalles Bibliográficos
Autores: Espínola García, Rafael, Pia̧tek, Bozėna
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2013
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/48490
Acceso en línea:http://hdl.handle.net/11441/48490
https://doi.org/10.1016/j.jmaa.2013.06.038
Access Level:acceso abierto
Palabra clave:Nonexpansive mappings
Fixed points
Unbounded convex sets
CAT(0) spaces
Banach-Steinhaus theorem
Descripción
Sumario: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.