Abstract
We introduce the notion of a 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.
Type
Publication
In Archiv der Mathematik
Armando W. Gutiérrez
Postdoctoral Researcher
Postdoctoral Researcher at Aalto University. My research interests are in metric geometry, functional analysis, optimization, and dynamics.