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

^*Corresponding author for this work

Not published at VTT

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

1 Downloads (Pure)

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
Journal	Archiv der Mathematik
Volume	119
Issue number	4
DOIs	https://doi.org/10.1007/s00013-022-01759-5
Publication status	Published - Oct 2022
MoE publication type	A1 Journal article-refereed

Funding

The first author acknowledges financial support from the Vilho, Yrjö and Kalle Väisälä Foundation of the Finnish Academy of Science and Letters, and from the Otto A. Malm Foundation.

Keywords

firm nonexpansive
firmly nonexpansive
metric functional
nonexpansive mapping
weak metric
metric spaces
metric geometry

Access to Document

10.1007/s00013-022-01759-5

firm-nonexpansiveAccepted author manuscript, 104 KB

Cite this

@article{eb29873f970444df87cdd3b9d4a8ecd9,

title = "Firm non-expansive mappings in weak metric spaces",

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.",

keywords = "firm nonexpansive, firmly nonexpansive, metric functional, nonexpansive mapping, weak metric, metric spaces, metric geometry",

author = "Guti{\'e}rrez, \{Armando W.\} and Cormac Walsh",

note = "Publisher Copyright: {\textcopyright} 2022, Springer Nature Switzerland AG.",

year = "2022",

month = oct,

doi = "10.1007/s00013-022-01759-5",

language = "English",

volume = "119",

pages = "389--400",

journal = "Archiv der Mathematik",

issn = "0003-889X",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - Firm non-expansive mappings in weak metric spaces

AU - Gutiérrez, Armando W.

AU - Walsh, Cormac

PY - 2022/10

Y1 - 2022/10

N2 - 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.

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.

KW - firm nonexpansive

KW - firmly nonexpansive

KW - metric functional

KW - nonexpansive mapping

KW - weak metric

KW - metric spaces

KW - metric geometry

UR - https://arxiv.org/abs/2110.13195

UR - https://zbmath.org/07589462

UR - https://www.scopus.com/pages/publications/85134715990

U2 - 10.1007/s00013-022-01759-5

DO - 10.1007/s00013-022-01759-5

M3 - Article

AN - SCOPUS:85134715990

SN - 0003-889X

VL - 119

SP - 389

EP - 400

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 4

ER -

Firm non-expansive mappings in weak metric spaces

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this