Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order. (English) Zbl 1220.46010
Summary: We prove that in a 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.
MSC:
| 46B20 | Geometry and structure of normed linear spaces |
| 46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |
Keywords:
modulus of convexity; set-valued mapping; uniform convexity; supporting function; generating set; strongly convex set of radius \(R\); Hilbert spaceReferences:
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