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...

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Detalles Bibliográficos
Autores: Ariza Ruiz, David, Leustean, Laurentiu, López Acedo, Genaro
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
Descripción
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.