Geodesic
Rotundity Properties, and Non-Extendability of Lipschitz Quasiconvex Functions
Journal of convex analysis, Tome 30 (2023) no. 1, pp. 329-342
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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.
Classification : 46A55, 52A05, 52A99, 26B25
Mots-clés : Lipschitz function, quasiconvex function, LUR point, exposing functional 
@article{JCA_2023_30_1_JCA_2023_30_1_a17,
     author = {C. A. De Bernardi and L. Vesely},
     title = {Rotundity {Properties,} and {Non-Extendability} of {Lipschitz} {Quasiconvex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {329--342},
     year = {2023},
     volume = {30},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a17/}
}
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C. A. De Bernardi; L. Vesely. Rotundity Properties, and Non-Extendability of Lipschitz Quasiconvex Functions. Journal of convex analysis, Tome 30 (2023) no. 1, pp. 329-342. http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a17/