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Asymptotically regular mappings in modular function spaces

 

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Author: Domínguez Benavides, Tomás
Khamsi, Mohamed Amine
Samadi, Sedki
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2001
Published in: Scientiae Mathematicae Japonicae, 4 (3), 239-248.
Document type: Article
Abstract: 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.
Cite: Domínguez Benavides, T., Khamsi, M.A. y Samadi, S. (2001). Asymptotically regular mappings in modular function spaces. Scientiae Mathematicae Japonicae, 4 (3), 239-248.
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URI: http://hdl.handle.net/11441/48921

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