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JOURNALS
// Matematicheskie Zametki
// Archive
Mat. Zametki,
1976
Volume 20,
Issue 2,
Pages
247–252
(Mi mzm9987)
This article is cited in
2
papers
Normed spaces which satisfy Apollonius' theorem
I. A. Danelich
Kursk Pedagogic State Institute
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.
UDC:
513.8
Received:
29.07.1975
Fulltext:
PDF file (658 kB)
Cited by
English version:
Mathematical Notes, 1976,
20
:2,
696–699
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