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Local characterization of strongly convex sets

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.

preprint2013arXivOpen access

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