Geodesic
Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 489-497.

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The well-known Tsar'kov's characterisation of finite-dimensional Banach spaces in which every bounded Chebyshev set (bounded $P$-acyclic set) is convex is extended to the asymmetrical setting. 
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A. R. Alimov. Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 489-497. http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a0/

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