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 Δ-convex functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-3-6,
author = {Marianna Cs\"ornyei and Assaf Naor},
title = {Lipschitz sums of convex functions},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {269-286},
zbl = {1059.52014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-3-6}
}
Marianna Csörnyei; Assaf Naor. Lipschitz sums of convex functions. Studia Mathematica, Tome 157 (2003) pp. 269-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-3-6/