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Firm non-expansive mappings in weak metric spaces

Authors :
Armando W. Gutiérrez
Cormac Walsh
TROPICAL (TROPICAL)
Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Vilho, Yrjö and Kalle Väisälä Foundation of the Finnish Academy of Science and Letters
Otto A. Malm Foundation
Source :
Archiv der Mathematik, Archiv der Mathematik, 2022, 119, pp.389-400
Publication Year :
2021

Abstract

We introduce the notion of firm non-expansive mapping in weak metric spaces, extending previous work for Banach spaces and certain geodesic spaces. We prove that, for firm non-expansive mappings, the minimal displacement, the linear rate of escape, and the asymptotic step size are all equal. This generalises a theorem by Reich and Shafrir.<br />12 pages. The new Section 3 contains a characterisation of the firm non-expansive mappings of one-dimensional asymmetric normed spaces. The reference list includes new entries. This version has been accepted by Archiv der Mathematik

Details

Language :
English
ISSN :
0003889X and 14208938
Database :
OpenAIRE
Journal :
Archiv der Mathematik, Archiv der Mathematik, 2022, 119, pp.389-400
Accession number :
edsair.doi.dedup.....48594f7a0e20d00851dc2f5edf3d0550