Firm non-expansive mappings in weak metric spaces

Armando W. Gutiérrez; Cormac Walsh

doi:10.1007/s00013-022-01759-5

Firm non-expansive mappings in weak metric spaces

Armando W. Gutiérrez
, Cormac Walsh

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	389-400
Number of pages	12
Journal	Archiv der Mathematik
Volume	119
Issue number	4
DOIs	https://doi.org/10.1007/s00013-022-01759-5
Publication status	Published - 1 Oct 2022

Keywords

Firm non-expansive
Firmly non-expansive
Metric functional
Non-expansive mapping
Weak metric

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10.1007/s00013-022-01759-5

Cite this

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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.",

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AB - 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.

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KW - Firmly non-expansive

KW - Metric functional

KW - Non-expansive mapping

KW - Weak metric

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Firm non-expansive mappings in weak metric spaces

Abstract

Keywords

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