Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 17 (2010), No. 2, 651--658Copyright Heldermann Verlag 2010 On Maximal Domains for C-Convex Functions and Convex Extensions Manfred Möller School of Mathematics, University of the Witwatersrand, Wits 2050, South Africa Manfred.Moller@wits.ac.za Thabang M. J. Nthebe School of Mathematics, University of the Witwatersrand, Wits 2050, South Africa Thabang.Nthebe@wits.ac.za [Abstract-pdf] \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 $\mathfrak{C}$. Keywords: Convex extension, C-convex, maximal set, CUP. MSC: 32E20, 35E10, 26A51, 46A55, 46S40, 52A41 [ Fulltext-pdf  (123  KB)] for subscribers only.