Subinvariant metric functionals for nonexpansive mappings

Armando W. Gutiérrez; Olavi Nevanlinna

doi:10.1080/01630563.2025.2528908

Subinvariant metric functionals for nonexpansive mappings

Armando W. Gutiérrez^*
, Olavi Nevanlinna

^*Corresponding author for this work

Aalto University

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

29 Downloads (Pure)

Abstract

We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed points of nonexpansive mappings. To demonstrate this, we additionally investigate subsets of Banach spaces that have only nontrivial metric functionals. We particularly show that in certain cases every metric functional has a unique minimizer; thus, subinvariance implies the existence of a fixed point.

Original language	English
Pages (from-to)	725-742
Number of pages	18
Journal	Numerical Functional Analysis and Optimization
Volume	46
Issue number	8-9
DOIs	https://doi.org/10.1080/01630563.2025.2528908
Publication status	Published - 15 Jul 2025
MoE publication type	A1 Journal article-refereed

Funding

A. W. Gutiérrez was supported by the Research Council of Finland (EasyDR project, grant 348093)

Keywords

nonexpansive mapping
common fixed point
metric functional
subinvariance
iterative methods
Banach spaces
metric spaces

Access to Document

10.1080/01630563.2025.2528908

SubinvariantMetricFunctionalsSubmitted manuscript, 393 KB
SubinvariantMetricFunctionals-AMversionAccepted author manuscript, 241 KB

Cite this

@article{4a4c00c8c39f446089d94a12fdd243f0,

title = "Subinvariant metric functionals for nonexpansive mappings",

abstract = "We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed points of nonexpansive mappings. To demonstrate this, we additionally investigate subsets of Banach spaces that have only nontrivial metric functionals. We particularly show that in certain cases every metric functional has a unique minimizer; thus, subinvariance implies the existence of a fixed point.",

keywords = "nonexpansive mapping, common fixed point, metric functional, subinvariance, iterative methods, Banach spaces, metric spaces",

author = "Guti{\'e}rrez, \{Armando W.\} and Olavi Nevanlinna",

note = "This is an Accepted Manuscript of an article published by Taylor \& Francis in Numerical Functional Analysis and Optimization on 15 July 2025, available at https://doi.org/10.1080/01630563.2025.2528908.",

year = "2025",

month = jul,

day = "15",

doi = "10.1080/01630563.2025.2528908",

language = "English",

volume = "46",

pages = "725--742",

journal = "Numerical Functional Analysis and Optimization",

issn = "0163-0563",

publisher = "Taylor \& Francis",

number = "8-9",

}

TY - JOUR

T1 - Subinvariant metric functionals for nonexpansive mappings

AU - Gutiérrez, Armando W.

AU - Nevanlinna, Olavi

N1 - This is an Accepted Manuscript of an article published by Taylor & Francis in Numerical Functional Analysis and Optimization on 15 July 2025, available at https://doi.org/10.1080/01630563.2025.2528908.

PY - 2025/7/15

Y1 - 2025/7/15

N2 - We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed points of nonexpansive mappings. To demonstrate this, we additionally investigate subsets of Banach spaces that have only nontrivial metric functionals. We particularly show that in certain cases every metric functional has a unique minimizer; thus, subinvariance implies the existence of a fixed point.

AB - We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed points of nonexpansive mappings. To demonstrate this, we additionally investigate subsets of Banach spaces that have only nontrivial metric functionals. We particularly show that in certain cases every metric functional has a unique minimizer; thus, subinvariance implies the existence of a fixed point.

KW - nonexpansive mapping

KW - common fixed point

KW - metric functional

KW - subinvariance

KW - iterative methods

KW - Banach spaces

KW - metric spaces

UR - https://www.scopus.com/pages/publications/105010947410

U2 - 10.1080/01630563.2025.2528908

DO - 10.1080/01630563.2025.2528908

M3 - Article

SN - 0163-0563

VL - 46

SP - 725

EP - 742

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 8-9

ER -

Subinvariant metric functionals for nonexpansive mappings

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

EasyDR: Enabling demand response through easy to use open source approach

Cite this

Subinvariant metric functionals for nonexpansive mappings

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Projects

EasyDR: Enabling demand response through easy to use open source approach

Cite this