Journal of Convex Analysis 30 (2023), No. 1, 329--342
Copyright Heldermann Verlag 2023
Rotundity Properties, and Non-Extendability of Lipschitz Quasiconvex Functions
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
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.
Keywords: Lipschitz function, quasiconvex function, LUR point, exposing functional.
MSC: 46A55, 52A05; 52A99, 26B25.
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