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...
| Autores: | , |
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| 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 |
| 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. |
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