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A note on Mosco convergence in $\operatorname {\mathrm {CAT}}(0)$ spaces

Part of: Miscellaneous applications of functional analysis Spaces with richer structures

Published online by Cambridge University Press:  17 January 2021

A. Bërdëllima Open the ORCID record for A. Bërdëllima [Opens in a new window]
A. Bërdëllima*
Affiliation:
Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany
*
e-mail: berdellima@math.tu-berlin.de
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Abstract

In this note, we show that in a complete $\operatorname {\mathrm {CAT}}(0)$ space pointwise convergence of proximal mappings under a certain normalization condition implies Mosco convergence.

Keywords

CAT(0) spacesMosco convergenceMoreau–Yosida approximateproximal mapping

MSC classification

Primary: 46N10: Applications in optimization, convex analysis, mathematical programming, economics
Secondary: 54E50: Complete metric spaces
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 4 , December 2022 , pp. 994 - 1003
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Copyright
© Canadian Mathematical Society, 2022

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