Right Bregman Nonexpansive Operators in Banach Spaces

By Victoria Martín-Márquez, Simeon Reich, Shoham Sabach. 2012

62 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6061fb85f52dcf79b2b0e21f196658a21a4bcbb8

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In Computational Theory and Mathematics

1. Shoham Sabach
2. Victoria Martín-Márquez
3. Simeon Reich
4. Dang Van Hieu
5. Aviv Gibali
6. Yekini Shehu
7. Oluwatosin Temitope Mewomo
8. Satit Saejung

In Geometry and Topology

1. Victoria Martín-Márquez
2. Shoham Sabach
3. Simeon Reich

In Numerical Analysis

1. Shoham Sabach
2. Victoria Martín-Márquez
3. Simeon Reich
4. Dang Van Hieu
5. Oluwatosin Temitope Mewomo
6. Duong Viet Thong
7. Yekini Shehu
8. Aviv Gibali

Citations in the corpus

• Bregman strongly nonexpansive operators in reflexive Banach spaces (2013, background): “We proved in [28] that the right Bregman projection −−→ projfKi is strictly R-BSNE.”