Alexander Weber and Gunther Reißig.
Local characterization of strongly convex sets.
J. Math. Anal. Appl., vol. 400, no. 2, Apr. 2013, pp. 743-750.
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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 δΩ of a set Ω. We also show that lim{ε → 0}δΩ(ε)/ε2 exists whenever Ω is closed and convex.
BibTeX entry:
@article{WeberReissig12,
  author  = {Alexander Weber and Gunther Rei{\ss}ig},
  title   = {Local characterization of strongly convex sets},
  journal = {J. Math. Anal. Appl.},
  year    = 2013,
  volume  = 400,
  number  = 2,
  pages   = {743-750},
  month   = apr,
  doi = {10.1016/j.jmaa.2012.10.071},
  eprint = {1207.4347}
}
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