On the product of the distances of a point from the vertices of a polytope |
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Authors: | Binyamin Schwarz |
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Institution: | (1) Technion - Israel Institute of Technology, Haifa |
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Abstract: | Letx
1,...,x
m be points in the solid unit sphere ofE
n and letx belong to the convex hull ofx
1,...,x
m. Then
. This implies that all such products are bounded by (2/m)
m
(m −1)
m−1. Bounds are also given for other normed linear spaces. As an application a bound is obtained for |p(z
0)| where
andp′(z
0)=0. |
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Keywords: | |
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