Abstract
In a normed spaceX, we consider objective functions which depend on the distances between a variable point and the points of certain finite setsA. A point where such a function attains its minimum onXis generically called an optimal location. In this paper we obtain characterizations of inner product spaces with properties connecting optimal locations and the convex hull ofAor barycenters of points ofAwith well chosen weights. We thus generalize several classical results about characterization of inner product spaces.
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