Geodesic
A Characterization of Strictly Convex Metric
Publications de l'Institut Mathématique, _N_S_39 (1986) no. 53, p. 149

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

A subset $G$ of a metric linear space $(E,d)$ is said to be semi-Chebyshev if each element of $E$ has at most approximation in $G$ and the space $(E,d)$ is said to be strictly convex if $d(x,0)\leq r$, $d(y,0) \leq r$ imply $d((x+y)/2,0) r$ unless $x=y$; $y\in E$ and $r$ is any positive real number. We prove that a metric linear space $(E,d)$ is strictly convex if and only if all convex subsets of $E$ are semi-Chebyshev.
Classification : 41A52 
@article{PIM_1986_N_S_39_53_a19,
     author = {T. D. Narang},
     title = {A {Characterization} of {Strictly} {Convex} {Metric}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {149 },
     publisher = {mathdoc},
     volume = {_N_S_39},
     number = {53},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1986_N_S_39_53_a19/}
}
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T. D. Narang. A Characterization of Strictly Convex Metric. Publications de l'Institut Mathématique, _N_S_39 (1986) no. 53, p. 149 . http://geodesic.mathdoc.fr/item/PIM_1986_N_S_39_53_a19/