Geodesic
On Maximal Domains for C-Convex Functions and Convex Extensions
Journal of convex analysis, Tome 17 (2010) no. 2, pp. 651-658

Voir la notice de l'article provenant de la source Heldermann Verlag

\newcommand\dom{\operatorname{dom}} Let $f$ be a real valued function with the domain $\dom(f)$ in some vector space $X$ and let $\mathfrak{C}$ be the collection of convex subsets of $X$. The following two questions are investigated; 1. Do there exist maximal convex restrictions $g$ of $f$ with $\dom(g) \in \mathfrak{C}$? 2. If $f$ is convex with $\dom(f)\in \mathfrak{C}$, do there exist maximal convex extension $g$ of $f$ with $\dom(g)\in \mathfrak{C}$? We will show that the answer to both questions is positive under a certain condition on $\mathfrak{C}$.
Classification : 32E20, 35E10, 26A51, 46A55, 46S40, 52A41
Mots-clés : Convex extension, C-convex, maximal set, CUP 
@article{JCA_2010_17_2_JCA_2010_17_2_a17,
     author = {M. M\"oller and T. M. J. Nthebe},
     title = {On {Maximal} {Domains} for {C-Convex} {Functions} and {Convex} {Extensions}},
     journal = {Journal of convex analysis},
     pages = {651--658},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a17/}
}
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M. Möller; T. M. J. Nthebe. On Maximal Domains for C-Convex Functions and Convex Extensions. Journal of convex analysis, Tome 17 (2010) no. 2, pp. 651-658. http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a17/