Artículo
Iterative methods for approximating fixed points of Bregman nonexpansive operators
Autor/es | Martín Márquez, Victoria
Reich, Simeon Sabach, Shoham |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2013-08 |
Fecha de depósito | 2016-10-07 |
Publicado en |
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Resumen | Diverse notions of nonexpansive type operators have been extended to the
more general framework of Bregman distances in reflexive Banach spaces. We study these classes of operators, mainly with respect to the existence ... Diverse notions of nonexpansive type operators have been extended to the more general framework of Bregman distances in reflexive Banach spaces. We study these classes of operators, mainly with respect to the existence and approximation of their (asymptotic) fixed points. In particular, the asymptotic behavior of Picard and Mann type iterations is discussed for quasi-Bregman nonexpansive operators. We also present parallel algorithms for approximating common fixed points of a finite family of Bregman strongly nonexpansive operators by means of a block operator which preserves the Bregman strong nonexpansivity. All the results hold, in particular, for the smaller class of Bregman firmly nonexpansive operators, a class which contains the generalized resolvents of monotone mappings with respect to the Bregman distance. |
Identificador del proyecto | MTM2009-13997-C02-01
FQM-127 647/07 |
Cita | Martín Márquez, V., Reich, S. y Sabach, S. (2013). Iterative methods for approximating fixed points of Bregman nonexpansive operators. Discrete and Continuous Dynamical Systems - Series S, 6 (4), 1043-1063. |
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