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Journal Articles Archiv der Mathematik Year : 2022

Firm non-expansive mappings in weak metric spaces

Armando W. Gutiérrez
  • Function : Author
Cormac Walsh

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.
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Dates and versions

hal-03479771 , version 1 (14-12-2021)
hal-03479771 , version 2 (12-07-2022)

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Armando W. Gutiérrez, Cormac Walsh. Firm non-expansive mappings in weak metric spaces. Archiv der Mathematik, 2022,  119, pp.389-400. ⟨hal-03479771v2⟩
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