Geodesic
On measure of nonconvexity and Jung constant
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 7, Tome 208 (1993), pp. 174-181

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For a Banach space $X$, a new constant $G(X)=\sup\{\lambda(A)\colon A\subset X,\ d(A)=1\}$ is introduced. The main result is that $G(X)$ coincides with the Jung constant $J(X)$ (Theorem 1), which yields an estimate for the latter. Some other results concerning $J(X)$ and the measure of nonconvexity $\lambda$ are given. Bibliography: 5 titles. 
@article{ZNSL_1993_208_a9,
     author = {N. M. Gulevich},
     title = {On measure of nonconvexity and {Jung} constant},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {174--181},
     publisher = {mathdoc},
     volume = {208},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_208_a9/}
}
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N. M. Gulevich. On measure of nonconvexity and Jung constant. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 7, Tome 208 (1993), pp. 174-181. http://geodesic.mathdoc.fr/item/ZNSL_1993_208_a9/