Article
Asymptotically nonexpansive mappings in modular function spaces
Author/s | Domínguez Benavides, Tomás
Khamsi, Mohamed Amine Samadi, Sedki |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2002-01-15 |
Deposit Date | 2016-09-22 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Dirección General de Investigación Científica y Técnica (DGICYT). España Junta de Andalucía |
Project ID. | PB-96-1338-C01-C02
PAI-FMQ-0127 |
Citation | Domínguez Benavides, T., Khamsi, M.A. y Samadi, S. (2002). Asymptotically nonexpansive mappings in modular function spaces. Journal of Mathematical Analysis and Applications, 265 (2), 249-263. |
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