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 $X$.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
