Right Bregman nonexpansive operators in Banach spaces
We introduce and study new classes of Bregman nonexpansive operators in reflexive Banach spaces. These classes of operators are associated with the Bregman distance induced by a convex function. In particular, we characterize sunny right quasi-Bregman nonexpansive retractions, and as a consequence w...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47199 |
| Acceso en línea: | http://hdl.handle.net/11441/47199 https://doi.org/10.1016/j.na.2012.04.048 |
| Access Level: | acceso abierto |
| Palabra clave: | Boltzmann-Shannon entropy Bregman distance Bregman firmly nonexpansive operator Fermi-Dirac entropy Legendre function Monotone mapping Nonexpansive operator Reflexive Banach space Resolvent Retraction T-monotone mapping Totally convex function |
| Sumario: | We introduce and study new classes of Bregman nonexpansive operators in reflexive Banach spaces. These classes of operators are associated with the Bregman distance induced by a convex function. In particular, we characterize sunny right quasi-Bregman nonexpansive retractions, and as a consequence we show that the fixed point set of any right quasi-Bregman nonexpansive operator is a sunny right quasi-Bregman nonexpansive retract of the ambient Banach space. |
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