Kuratowski measure of noncompactness as a distance

In the paper we introduce the concept of the Kuratowski distance between nonempty and bounded subsets of a Banach space. We show that the Kuratowski measure of noncompactness of a nonempty and bounded subset of a Banach space is equal to the Kuratowski distance of that subset to the family of all nonempty and relatively compact subsets of the mentioned Banach space.

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Publication Details

Journal
Nonlinear Analysis
Published
2026-09-22
DOI
https://doi.org/10.1016/j.na.2026.114280
Primary Topic
Nonlinear Differential Equations Analysis
Type
article
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article

Kuratowski measure of noncompactness as a distance

Józef Banaś, Antonio Martinón
Nonlinear Analysis
Nonlinear Differential Equations Analysis
article

Kuratowski measure of noncompactness as a distance

Józef Banaś, Antonio Martinón
article en

Abstract

In the paper we introduce the concept of the Kuratowski distance between nonempty and bounded subsets of a Banach space. We show that the Kuratowski measure of noncompactness of a nonempty and bounded subset of a Banach space is equal to the Kuratowski distance of that subset to the family of all nonempty and relatively compact subsets of the mentioned Banach space.

Nonlinear AnalysisVol. 275
Rzeszów University of Technology (PL), Universidad de La Laguna (ES)
Reduced inequalities
Openalex Percentile: Top 6%
Nonlinear Differential Equations Analysis
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