Characterizations of inner product spaces by means of norm one points - Mendoza, José; Pakhrou, Tijani (Mathematica Scandinavica, 2005)
Let X be a a real normed linear space of dimension at least three, with unit sphere S_X. In this paper we prove that X is an inner product space if and only if every three point subset of S_X has a Chebyshev center in its convex hull. We also give other characterizations expressed in terms of centers of three point subsets of S_X only. We use in these characterizations Chebyshev centers as well as Fermat centers and p-centers.