Transactions of the American Mathematical Society

Author(s): Carlos Benítez; Manuel Fernández; María L. Soriano
Journal: Trans. Amer. Math. Soc. 354 (2002), 5027-5038.
MSC (2000): Primary 46B20, 46C15, 90B85
Posted: August 1, 2002
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Abstract: We prove that a real normed space

with $\dim X\ge 3$ is an inner product space if and only if, for every three points $u,v,w\in X$ , the set of points at which the function $x\in X\to \Vert u-x\Vert+\Vert v-x\Vert+\Vert w-x\Vert$ 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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Carlos Benítez
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain
Email: cabero@unex.es

Manuel Fernández
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain
Email: ghierro@unex.es

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