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arXiv · 1101.5685

Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order

Maxim V. Balashov·Dušan Repovš
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Abstract

We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.

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Maxim V. Balashov, Dušan Repovš. 2011-01-29. Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order. https://doi.org/10.1016/j.jmaa.2010.11.046

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