Firm non-expansive mappings in weak metric spaces

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.

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

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