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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 2, Pages 45–58 (Mi ivm8973)  
This article is cited in 5 scientific papers (total in 5 papers)

On asphericity of convex body

S. I. Dudov, E. A. Meshcheryakova

Chair of Mathematical Economics, Saratov State University, 83 Astrakhanskaya str., Saratov, 410012 Russia
Full-text PDF (240 kB) Citations (5)
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Abstract: The paper deals with a finite-dimensional problem of minimizing for a given convex body the ratio of the circumscribed ball radius to the inscribed ball radius (in an arbitrary norm) by choosing the common center of these balls. We establish quasiconvexity and subdifferentiability of the objective function of this problem. We find a criterion of a solution and conditions of its uniqueness. The main problem is compared with problems which are close to it in geometric sense.
Keywords: asphericity, convex body, subdifferential, quasiconvexity, uniform estimate.
Received: 22.06.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 2, Pages 36–47
DOI: https://doi.org/10.3103/S1066369X15020061
Bibliographic databases:
Document Type: Article
UDC: 519.853
Language: Russian
Citation: S. I. Dudov, E. A. Meshcheryakova, “On asphericity of convex body”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 2, 45–58; Russian Math. (Iz. VUZ), 59:2 (2015), 36–47
Citation in format AMSBIB
\Bibitem{DudMes15}
\by S.~I.~Dudov, E.~A.~Meshcheryakova
\paper On asphericity of convex body
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 2
\pages 45--58
\mathnet{http://mi.mathnet.ru/ivm8973}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 2
\pages 36--47
\crossref{https://doi.org/10.3103/S1066369X15020061}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84921875693}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:61
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