Geodesic
Metrically convex functions in normed spaces
Studia Mathematica, Tome 105 (1993) no. 1, pp. 1-11
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Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory. 
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Stanisław Kryński. Metrically convex functions in normed spaces. Studia Mathematica, Tome 105 (1993) no. 1, pp. 1-11. doi: 10.4064/sm-105-1-1-11

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