Uniformly Lipschitzian mappings in modular function spaces
Let ρ be a convex modular function satisfying a ∆2-type condition and Lρ the corresponding modular space. Assume that C is a ρ-bounded and ρ-a.e compact subset of Lρ and T : C → C is a k-uniformly Lipschitzian mapping. We prove that T has a fixed point if k < (Ñ(Lρ))−1/2 where Ñ(Lρ) is a geometri...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2001 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/45280 |
| Acesso em linha: | http://hdl.handle.net/11441/45280 https://doi.org/10.1016/S0362-546X(00)00117-6 |
| Access Level: | acceso abierto |
| Palavra-chave: | Uniformly Lipschitzian mappings Fixed point Modular functions Uniform normal stucture Uniform convex Orlicz function Modulus of convexity |
| Resumo: | Let ρ be a convex modular function satisfying a ∆2-type condition and Lρ the corresponding modular space. Assume that C is a ρ-bounded and ρ-a.e compact subset of Lρ and T : C → C is a k-uniformly Lipschitzian mapping. We prove that T has a fixed point if k < (Ñ(Lρ))−1/2 where Ñ(Lρ) is a geometrical coefficient of normal structure. We also show that Ñ(Lρ) < 1 in modular Orlicz spaces for uniformly convex Orlicz functions. |
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