Geodesic
A relation between Jensen's inequality and a geometrical problem
Matematičeskie zametki, Tome 3 (1968) no. 3, pp. 327-338 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{MZM_1968_3_3_a11,
     author = {V. I. Berdyshev},
     title = {A~relation between {Jensen's} inequality and a~geometrical problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {327--338},
     year = {1968},
     volume = {3},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_3_a11/}
}
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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/