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Matematicheskie Zametki, 1968, Volume 3, Issue 3, Pages 327–338 (Mi mzm6685)  
This article is cited in 11 scientific papers (total in 11 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
Full-text PDF (699 kB) Citations (11)
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.
Received: 12.06.1967
English version:
Mathematical Notes, 1968, Volume 3, Issue 3, Pages 206–213
DOI: https://doi.org/10.1007/BF01387336
Bibliographic databases:
UDC: 517.5
Language: Russian
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/mzm6685}
\mathscinet{http://mathscinet.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}
Linking options:
  • https://www.mathnet.ru/eng/mzm6685
  • https://www.mathnet.ru/eng/mzm/v3/i3/p327
    • This publication is cited in the following 11 articles:
    1. 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  zmath  adsnasa  isi  elib
    2. Ivanov G.M., “Uklonenie vypukloi obolochki ogranichennykh mnozhestv”, Trudy moskovskogo fiziko-tekhnicheskogo instituta, 2012, 105–112 Deviation of the convex hull of bounded sets  elib
    3. 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
    4. “Vitalii Ivanovich Berdyshev”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S1–S9  mathnet  crossref  isi
    5. E. V. Manokhin, “Nekotorye mnozhestva ln1 i konstanta Yunga”, Chebyshevskii sb., 9:1 (2008), 144–147  mathnet  mathscinet
    6. Ya Qiang Yan, “Exact Values of Some Geometric Constants of Orlicz Spaces”, Acta Math Sinica, 23:5 (2007), 827  crossref
    7. 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
    8. Applications Of Orlicz Spaces, 2002  crossref
    9. 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
    10. V. I. Ivanov, “On the relation between the Jackson and Jung constants of the spaces Lp”, Math. Notes, 58:6 (1995), 1269–1275  mathnet  crossref  mathscinet  zmath  isi
    11. N. P. Korneichuk, “On extremal problems in the theory of best approximation”, Russian Math. Surveys, 29:3 (1974), 7–43  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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