Convexity of out-Chebyshev sets

A. R. Alimov; N. A. Il’yasov

doi:10.32010/j.bmj.2025.16

September 25, 2025Baku Mathematical JournalOpen Access

Convexity of out-Chebyshev sets

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Key Points

The study shows that out-Chebyshev sets maintain convexity in higher dimensions, enhancing understanding of approximations.
Key evidence includes the application of the classical theorem to out-Chebyshev sets, establishing their unique best approximant.
This analysis involves extending existing theoretical frameworks, particularly the Berdyshev–Brøndsted–Brown theorem.
The findings highlight the significance of convexity in approximation theory, inviting further exploration of such sets.

Implication

This work extends the berdyshev-brøndsted-brown theorem on convexity and explores out-chebyshev sets.

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.

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Cite This Study

Alimov et al. (2025) studied this question.

synapsesocial.com/papers/68d7cc6aeebfec0fc5238e51 https://doi.org/10.32010/j.bmj.2025.16

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Convexity of out-Chebyshev sets

Key Points

Implication

Abstract

Discussion

Cite This Study

Convexity of out-Chebyshev sets

Key Points

Implication

Abstract

Discussion

Cite This Study

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