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...
| Autores: | , , |
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| 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 |
| 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. |
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