Asymptotically nonexpansive mappings in modular function spaces
In this paper, we prove that if ρ is a convex, σ-finite modular function satisfying a ∆2-type condition, C a convex, ρ-bounded, ρ-a.e. compact subset of Lρ and T : C → C a ρ-asymptotically nonexpansive mapping, then T has a fixed point. In particular, any asymptotically nonexpansive self-map defined...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2002 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/45283 |
| Acceso en línea: | http://hdl.handle.net/11441/45283 https://doi.org/10.1006/jmaa.2000.7275 |
| Access Level: | acceso abierto |
| Palabra clave: | Asymptotically nonexpansive mappings Fixed point Modular functions |
| Sumario: | In this paper, we prove that if ρ is a convex, σ-finite modular function satisfying a ∆2-type condition, C a convex, ρ-bounded, ρ-a.e. compact subset of Lρ and T : C → C a ρ-asymptotically nonexpansive mapping, then T has a fixed point. In particular, any asymptotically nonexpansive self-map defined on a convex subset of L1 (Ω, µ) which is compact for the topology of local convergence in measure has a fixed point. |
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