Firmly nonexpansive mappings in classes of geodesic spaces
Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different cla...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42604 |
| Acceso en línea: | http://hdl.handle.net/11441/42604 https://doi.org/10.1090/S0002-9947-2014-05968-0 |
| Access Level: | acceso abierto |
| Palabra clave: | firmly nonexpansive mappings geodesic spaces uniform convexity Picard iterates asymptotic regularity ∆-convergence proof mining effective bounds minimization problems |
| Sumario: | Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations. |
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