Asymptotically regular mappings in modular function spaces
Let ρ be a modular function satisfying a ∆2-type condition and Lρ the corresponding modular space. The main result in this paper states that if C is a ρ-bounded and ρ-a.e sequentially compact subset of Lρ and T : C → C is an asymptotically regular mapping such that lim inf n→∞ [Tn] < 2, where |S|...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versión enviada para evaluación y publicación |
| Data de publicação: | 2001 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/48921 |
| Acesso em linha: | http://hdl.handle.net/11441/48921 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Asymptotically regular mappings Fixed point Modular functions Opial property |
| Resumo: | Let ρ be a modular function satisfying a ∆2-type condition and Lρ the corresponding modular space. The main result in this paper states that if C is a ρ-bounded and ρ-a.e sequentially compact subset of Lρ and T : C → C is an asymptotically regular mapping such that lim inf n→∞ [Tn] < 2, where |S| denotes the Lipschitz constant of S, then T has a fixed point. We show that the estimate lim inf n→∞ [Tn] < 2 cannot be, in general, improved. |
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