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Journal of Convex Analysis 25 (2018), No. 3, 737--758
Copyright Heldermann Verlag 2018

Normal Regularity of Weakly Convex Sets in Asymmetric Normed Spaces

Mariana S. Lopushanski
Department of Higher Mathematics, Moscow Institute of Physics and Technology, Institutski str. 9, Dolgoprudny -- Moscow region, Russia 141700

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.

Keywords: Duality mapping, weakly convex set, Fréchet normal regular, proximally normal regular.

MSC: 58C06, 58C20, 49J52

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