Abstract
We prove that a real normed space X with dim X ≥ 3 is an inner product space if and only if, for every three points u,v,w E X, the set of points at which the function x ∈ X → ∥u - x∥ + ∥v - x∥ + ∥w - x∥ attains its minimum (called the set of Fermat-Torricelli medians of the three points) intersects the convex hull of these three points.
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