Abstract

We consider duality mappings in asymmetric normed spaces and study their properties. We also prove the Fréchet normal regularity and the proximally normal regularity of weakly convex sets in asymmetric normed spaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Mariana S. Lopushanski

Department of Higher Mathematics, Moscow Institute of Physics and Technology, Institutski str. 9, Dolgoprudny – Moscow region, Russia 141700

masha.alexandra@gmail.com

Keywords

  • Duality mapping
  • weakly convex set
  • Fréchet normal regular
  • proximally normal regular

Mathematics Subject Classification

58C06, 58C20, 49J52

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Suggested citation

M. S. Lopushanski. “Normal Regularity of Weakly Convex Sets in Asymmetric Normed Spaces.” Journal of Convex Analysis 25 (2018), No. 3, 737–758. https://doi.org/10.68381/jca25051

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press LLC.