Convexity of out-Chebyshev sets

A set is an out-Chebyshev set if any point lying at a positive distance from this set has a unique best approximant in this set. We extend the classical Berdyshev– Brøndsted–Brown theorem on convexity of Chebyshev sets in spaces of dimension 4 to the case of out-Chebyshev sets.

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Publication Details

Journal
Baku Mathematical Journal
Published
2025-09-25
DOI
https://doi.org/10.32010/j.bmj.2025.16
Primary Topic
Optimization and Variational Analysis
Type
article
Field-Weighted Citation Impact
0.00

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article

Convexity of out-Chebyshev sets

N. A. Il’yasov, A. R. Alimov
Baku Mathematical Journal
Optimization and Variational Analysis
article

Convexity of out-Chebyshev sets

N. A. Il’yasov, A. R. Alimov
article en

Abstract

A set is an out-Chebyshev set if any point lying at a positive distance from this set has a unique best approximant in this set. We extend the classical Berdyshev– Brøndsted–Brown theorem on convexity of Chebyshev sets in spaces of dimension 4 to the case of out-Chebyshev sets.

Baku Mathematical JournalVol. 4(2)
Ministry of Science and Higher Education of the Russian Federation
Openalex Percentile: Top 72%
Optimization and Variational Analysis
DOIOpen Access PDFOpenAlex
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Convexity of out-Chebyshev sets — N. A. Il’yasov, A. R. Alimov · Baku Mathematical Journal (2025) | TGRS Research Map | TGRS