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 $f\colon A\to \R$ not admitting any continuous quasiconvex extension to the whole $X$.

De Bernardi, C. A., Vesely, L., Rotundity Properties, and Non-Extendability of Lipschitz Quasiconvex Functions, <<JOURNAL OF CONVEX ANALYSIS>>, 2023; 2023 (30): 329-342 [https://hdl.handle.net/10807/230167]

Rotundity Properties, and Non-Extendability of Lipschitz Quasiconvex Functions

De Bernardi, Carlo Alberto;
2023

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 $f\colon A\to \R$ not admitting any continuous quasiconvex extension to the whole $X$.
2023
Inglese
De Bernardi, C. A., Vesely, L., Rotundity Properties, and Non-Extendability of Lipschitz Quasiconvex Functions, <<JOURNAL OF CONVEX ANALYSIS>>, 2023; 2023 (30): 329-342 [https://hdl.handle.net/10807/230167]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/230167
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