Fixed point theorems in R-trees with applications to graph theory
It is proved that a commutative family of nonexpansive mappings of a complete -tree X into itself always has a nonempty common fixed point set if X does not contain a geodesic ray. As a consequence of this, we show that any commuting family of edge preserving mappings of a connected reflexive graph...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/181662 |
| Acceso en línea: | https://hdl.handle.net/11441/181662 https://doi.org/10.1016/j.topol.2005.03.001 |
| Access Level: | acceso abierto |
| Palabra clave: | Fixed points Nonexpansive mappings R-trees Fixed edge theorem |
| Sumario: | It is proved that a commutative family of nonexpansive mappings of a complete -tree X into itself always has a nonempty common fixed point set if X does not contain a geodesic ray. As a consequence of this, we show that any commuting family of edge preserving mappings of a connected reflexive graph G that contains no cycles or infinite paths always has at least one common fixed edge. This approach provides a new proof of the classical fixed edge theorem of Nowakowski and Rival. Several related results are also obtained. |
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