Characterizations of inner product spaces by means of norm one points
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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.
2010 ◽
Vol 47
(4)
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pp. 505-512
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2004 ◽
Vol 69
(2)
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pp. 327-340
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2021 ◽
Vol 3
(2)
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pp. 80
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1981 ◽
Vol 24
(2)
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pp. 239-246
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2005 ◽
Vol 2005
(18)
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pp. 2883-2893
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2005 ◽
Vol 78
(2)
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pp. 199-210
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