A~relation between Jensen's inequality and a~geometrical problem
Matematičeskie zametki, Tome 3 (1968) no. 3, pp. 327-338.

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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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     author = {V. I. Berdyshev},
     title = {A~relation between {Jensen's} inequality and a~geometrical problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {327--338},
     publisher = {mathdoc},
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     year = {1968},
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V. I. Berdyshev. A~relation between Jensen's inequality and a~geometrical problem. Matematičeskie zametki, Tome 3 (1968) no. 3, pp. 327-338. http://geodesic.mathdoc.fr/item/MZM_1968_3_3_a11/