Bregman strongly nonexpansive operators in reflexive Banach spaces

We present a detailed study of right and left Bregman strongly nonexpansive operators in reflexive Banach spaces. We analyze, in particular, compositions and convex combinations of such operators, and prove the convergence of the Picard iterative method for operators of these types. Finally, we use...

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Detalles Bibliográficos
Autores: Martín Márquez, Victoria, Reich, Simeon, Sabach, Shoham
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2013
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/44797
Acceso en línea:http://hdl.handle.net/11441/44797
https://doi.org/10.1016/j.jmaa.2012.11.059
Access Level:acceso abierto
Palabra clave:Bregman distance
Bregman strongly nonexpansive operator
Legendre function
Monotone mapping
Nonexpansive operator
Reflexive Banach space
Resolvent
Totally convex function
Descripción
Sumario:We present a detailed study of right and left Bregman strongly nonexpansive operators in reflexive Banach spaces. We analyze, in particular, compositions and convex combinations of such operators, and prove the convergence of the Picard iterative method for operators of these types. Finally, we use our results to approximate common zeroes of maximal monotone mappings and solutions to convex feasibility problems.