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math.FA2011★ 20 cited
Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order
Maxim V. Balashov, Dušan Repovš
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 obta…
math.FA2010★ 7 cited
Polyhedral approximations of strictly convex compacta
Maxim V. Balashov, Dušan Repovš
We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible esti…
math.FA2010★ 7 cited
Weakly convex sets and modulus of nonconvexity
Maxim V. Balashov, Dušan Repovš
We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clar…