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 : A → R not admitting any continuous quasiconvex extension to the whole X.
Rotundity properties, and non-extendability of Lipschitz quasiconvex functions / C.A. De Bernardi, L. Vesely. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 30:1(2023), pp. 329-342.
Rotundity properties, and non-extendability of Lipschitz quasiconvex functions
L. VeselyUltimo
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 : A → R not admitting any continuous quasiconvex extension to the whole X.
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