Local characterization of strongly convex sets

Abstract

Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity δ_Ωof a set Ω. We also show that \lim_{ε\to 0} δ_Ω(ε)/ε^2 exists whenever Ωis closed and convex.

References in corpus (2)

• Uniform convexity and the splitting problem for selections
• Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order