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Mat. Zametki, 1968, Volume 3, Issue 3, Pages 327–338 (Mi mz6685)  

This article is cited in 9 scientific papers (total in 9 papers)

A relation between Jensen's inequality and a geometrical problem

V. I. Berdyshev

V. A. Steklov Institute of Mathematics, Sverdlovsk Branch of the Academy of Sciences of USSR

Abstract: A relation is established between Jensen's inequality and a problem suggested by H. Jung concerning the size of the smallest sphere containing a set of given diameter. An estimate is obtained of the size of this sphere in terms of the absolute value of the convexity of the space.

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English version:
Mathematical Notes, 1968, 3:3, 206–213

Bibliographic databases:

UDC: 517.5
Received: 12.06.1967

Citation: V. I. Berdyshev, “A relation between Jensen's inequality and a geometrical problem”, Mat. Zametki, 3:3 (1968), 327–338; Math. Notes, 3:3 (1968), 206–213

Citation in format AMSBIB
\Bibitem{Ber68}
\by V.~I.~Berdyshev
\paper A~relation between Jensen's inequality and a~geometrical problem
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 3
\pages 327--338
\mathnet{http://mi.mathnet.ru/mz6685}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=230021}
\zmath{https://zbmath.org/?q=an:0179.45603|0179.45602}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 3
\pages 206--213
\crossref{https://doi.org/10.1007/BF01387336}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. P. Korneichuk, “On extremal problems in the theory of best approximation”, Russian Math. Surveys, 29:3 (1974), 7–43  mathnet  crossref  mathscinet  zmath
    2. V. I. Ivanov, “On the relation between the Jackson and Jung constants of the spaces $L_ p$”, Math. Notes, 58:6 (1995), 1269–1275  mathnet  crossref  mathscinet  zmath  isi
    3. V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. V. Nguyen-Khac, K. Nguyen-Van, “An Infinite-Dimensional Generalization of the Jung theorem”, Math. Notes, 80:2 (2006), 224–243  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. E. V. Manokhin, “Nekotorye mnozhestva $l_1^n$ i konstanta Yunga”, Chebyshevskii sb., 9:1 (2008), 144–147  mathnet  mathscinet
    6. “Vitalii Ivanovich Berdyshev”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S1–S9  mathnet  crossref  isi
    7. Ivanov G.M., “Uklonenie vypukloi obolochki ogranichennykh mnozhestv”, Trudy moskovskogo fiziko-tekhnicheskogo instituta, 2012, 105–112  elib
    8. Manokhin E.V., “Konstanty yunga proizvedenii nekotorykh prostranstv banakha”, Sbornik nauchnykh trudov sworld po materialam mezhdunarodnoi nauchno-prakticheskoi konferentsii, 2:3 (2012), 70–76  elib
    9. A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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