Abstract

Let A be an open convex subset of a real normed linear space X. We prove that if the boundary of A contains a non-LUR point then there exists a Lipschitz quasiconvex function f from A to R not admitting any continuous quasiconvex extension to the whole X.

Author information

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

Carlo Alberto De Bernardi

Dip. di Matematica per le Scienze Economiche, Finanziarie ed Attuariali, Università Cattolica del Sacro Cuore, Milano, Italy

carloalberto.debernardi@unicatt.it

Libor Vesely

Dip. di Matematica "F. Enriques", Università degli Studi di Milano, Italy

libor.vesely@unimi.it

Keywords

  • Lipschitz function
  • quasiconvex function
  • LUR point
  • exposing functional

Mathematics Subject Classification

46A55, 52A05; 52A99, 26B25

Suggested citation

C. A. De Bernardi, L. Vesely. “Rotundity Properties, and Non-Extendability of Lipschitz Quasiconvex Functions.” Journal of Convex Analysis 30 (2023), No. 1, 329–342.

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