[Banach] Abstract of a paper by Maxim V. Balashov and Dusan Repovs

This is an announcement for the paper "Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order" by Maxim V. Balashov and Dusan Repovs.

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.

Archive classification: math.FA math.GN

Mathematics Subject Classification: 46C05, 54C60, 46N10, 32F17

Citation: J. Math. Anal. Appl. 377:2 (2011), 754-761

Submitted from: dusan.repovs@guest.arnes.si

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1101.5685

or

http://arXiv.org/abs/1101.5685