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Matematicheskie Zametki, 2023, Volume 113, Issue 6, Pages 905–917
DOI: https://doi.org/10.4213/mzm13628 (Mi mzm13628) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Chebyshev Sets with Piecewise Continuous Metric Projection

I. G. Tsar'kovab

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
Full-text PDF (585 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm13628
Abstract: We study the properties of Chebyshev sets composed of at most countably many sets with a continuous metric projection. Local solarity is established in neighborhoods on which the metric projection is single-valued and continuous in uniformly convex spaces. As examples of applications of the results obtained, we consider generalized fractions and products, as well as ridge functions.
Keywords: uniformly convex spaces, metric projection, Chebyshev sets, local solarity.
Funding agency Grant number
Russian Science Foundation 22-21-00204
The study was carried out at Lomonosov Moscow State University and was supported by the Russian Science Foundation under grant no. 22-21-00204, https://rscf.ru/project/22-21-00204/.
Received: 23.06.2022
Revised: 27.10.2022
Published: 01.06.2023
English version:
Mathematical Notes, 2023, Volume 113, Issue 6, Pages 840–849
DOI: https://doi.org/10.1134/S0001434623050255
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
MSC: 41A65
Language: Russian
Citation: I. G. Tsar'kov, “Chebyshev Sets with Piecewise Continuous Metric Projection”, Mat. Zametki, 113:6 (2023), 905–917; Math. Notes, 113:6 (2023), 840–849
Citation in format AMSBIB
\Bibitem{Tsa23}
\by I.~G.~Tsar'kov
\paper Chebyshev Sets with Piecewise Continuous Metric Projection
\jour Mat. Zametki
\yr 2023
\vol 113
\issue 6
\pages 905--917
\mathnet{http://mi.mathnet.ru/mzm13628}
\crossref{https://doi.org/10.4213/mzm13628}
\transl
\jour Math. Notes
\yr 2023
\vol 113
\issue 6
\pages 840--849
\crossref{https://doi.org/10.1134/S0001434623050255}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85163199180}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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