Resumen de Characterizations of inner product spaces by means of norm one points

J. Mendoza, Tijani Pakhrou

• Let X be a a real normed linear space of dimension at least three, with unit sphere SX. In this paper we prove that X is an inner product space if and only if every three point subset of SX has a Chebyshev center in its convex hull. We also give other characterizations expressed in terms of centers of three point subsets of SX only. We use in these characterizations Chebyshev centers as well as Fermat centers and p-centers.