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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 5, Pages 22–38
DOI: https://doi.org/10.26907/0021-3446-2020-5-22-38
(Mi ivm9568)
 

This article is cited in 1 scientific paper (total in 1 paper)

Properties of the distance function to strongly and weakly convex sets in a nonsymmetrical space

S. I. Dudova, E. S. Polovinkinb, V. V. Abramovaa

a Saratov National Research State University, 83 Astrakhanskaya str., Saratov, 410012 Russia
b Moscow Institute of Physics and Technology (National Research University), 9 Institutskiy per., Dolgoprudnyi, Moscow region, 141700 Russia
Full-text PDF (415 kB) Citations (1)
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Abstract: We consider the distance function (DF), given by the caliber (the Minkowski gauge function) of a convex body, from a point to strictly, strongly and weakly convex sets in an arbitrary Hilbert space. Some properties of the caliber of a strongly convex set and the conditions for obtaining a strict, strong or weak convexity of Lebesgue sets of the distance function are established in accordance with the requirements for the set, the caliber of which specifies the distance function, and the set to which the distance is measured. The corresponding inequalities are obtained that reflect the behavior of the distance function on segments and allow comparing it with strictly, strongly or weakly convex functions.
Keywords: gauge of a set, distance function (DF), strongly and weakly convex sets and functions.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00209_а
Received: 25.04.2019
Revised: 29.07.2019
Accepted: 25.09.2019
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 5, Pages 17–30
DOI: https://doi.org/10.3103/S1066369X20050035
Bibliographic databases:
Document Type: Article
UDC: 519.853
Language: Russian
Citation: S. I. Dudov, E. S. Polovinkin, V. V. Abramova, “Properties of the distance function to strongly and weakly convex sets in a nonsymmetrical space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 5, 22–38; Russian Math. (Iz. VUZ), 64:5 (2020), 17–30
Citation in format AMSBIB
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\by S.~I.~Dudov, E.~S.~Polovinkin, V.~V.~Abramova
\paper Properties of the distance function to strongly and weakly convex sets in a nonsymmetrical space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 5
\pages 22--38
\mathnet{http://mi.mathnet.ru/ivm9568}
\crossref{https://doi.org/10.26907/0021-3446-2020-5-22-38}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2020
\vol 64
\issue 5
\pages 17--30
\crossref{https://doi.org/10.3103/S1066369X20050035}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85086841991}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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