Firm non-expansive mappings in weak metric spaces
Metric Geometry
2022-12-29 v2
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.
Keywords
Cite
@article{arxiv.2110.13195,
title = {Firm non-expansive mappings in weak metric spaces},
author = {Armando W. Gutiérrez and Cormac Walsh},
journal= {arXiv preprint arXiv:2110.13195},
year = {2022}
}
Comments
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