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Matematicheskie Zametki, 1976, Volume 20, Issue 2, Pages 247–252 (Mi mzm9987)  
This article is cited in 2 scientific papers (total in 2 papers)

Normed spaces which satisfy Apollonius' theorem

I. A. Danelich

Kursk Pedagogic State Institute
Full-text PDF (658 kB) Citations (2)
Abstract: It is proved that a normed space is a Hilbert space if it possesses the property: The geometric locus of the points, for which the ratio of the distances to two given points is constant, is a sphere.
Received: 29.07.1975
English version:
Mathematical Notes, 1976, Volume 20, Issue 2, Pages 696–699
DOI: https://doi.org/10.1007/BF01155877
Bibliographic databases:
Document Type: Article
UDC: 513.8
Language: Russian
Citation: I. A. Danelich, “Normed spaces which satisfy Apollonius' theorem”, Mat. Zametki, 20:2 (1976), 247–252; Math. Notes, 20:2 (1976), 696–699
Citation in format AMSBIB
\Bibitem{Dan76}
\by I.~A.~Danelich
\paper Normed spaces which satisfy Apollonius' theorem
\jour Mat. Zametki
\yr 1976
\vol 20
\issue 2
\pages 247--252
\mathnet{http://mi.mathnet.ru/mzm9987}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=435810}
\zmath{https://zbmath.org/?q=an:0343.46013}
\transl
\jour Math. Notes
\yr 1976
\vol 20
\issue 2
\pages 696--699
\crossref{https://doi.org/10.1007/BF01155877}
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  • https://www.mathnet.ru/eng/mzm/v20/i2/p247
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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