Right Bregman nonexpansive operators in Banach spaces |
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Authors: | Victoria Martín-Márquez Simeon Reich Shoham Sabach |
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Institution: | 1. Departamento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain;2. Department of Mathematics, The Technion–Israel Institute of Technology, 32000 Haifa, Israel |
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Abstract: | 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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Keywords: | 26B25 46T99 47H04 47H05 47H09 47H10 52A41 54C15 |
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