Comments on the cosmic convergence of nonexpansive maps

Armando W. Gutiérrez; Anders Karlsson

doi:10.1007/s11784-021-00896-8

Comments on the cosmic convergence of nonexpansive maps

Armando W. Gutiérrez^*
, Anders Karlsson

^*Corresponding author for this work

Not published at VTT

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

3 Citations (Scopus)

Abstract

This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of ℓ¹. We also point out some inaccurate assertions appearing in the literature on this topic.

Original language	English
Article number	59
Journal	Journal of Fixed Point Theory and Applications
Volume	23
Issue number	4
DOIs	https://doi.org/10.1007/s11784-021-00896-8
Publication status	Published - Nov 2021
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. The second author acknowledges partial financial support from the Swiss NSF grant 200020_15958.

Keywords

invariant subspace
fixed points
metric functional
nonexpansive mapping

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10.1007/s11784-021-00896-8Licence: CC BY

Cite this

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title = "Comments on the cosmic convergence of nonexpansive maps",

abstract = "This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of ℓ1. We also point out some inaccurate assertions appearing in the literature on this topic.",

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AU - Gutiérrez, Armando W.

AU - Karlsson, Anders

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AB - This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of ℓ1. We also point out some inaccurate assertions appearing in the literature on this topic.

KW - invariant subspace

KW - fixed points

KW - metric functional

KW - nonexpansive mapping

UR - https://arxiv.org/abs/2103.14499

UR - https://zbmath.org/07419640

UR - https://www.scopus.com/pages/publications/85114446226

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JO - Journal of Fixed Point Theory and Applications

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Comments on the cosmic convergence of nonexpansive maps

Abstract

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Keywords

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