Lipschitz sums of convex functions
Volume 158 / 2003
Studia Mathematica 158 (2003), 269-286
MSC: 52A41, 26B25.
DOI: 10.4064/sm158-3-6
Abstract
We give a geometric characterization of the convex subsets of a Banach space with the property that for any two convex continuous functions on this set, if their sum is Lipschitz, then the functions must be Lipschitz. We apply this result to the theory of ${\mit \Delta }$-convex functions.
