This article is cited 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

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.

UDC: 517.5

Received: 12.06.1967

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

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