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.
All Science Journal Classification (ASJC) codes
- Convex functions
- Lipschitz functions
- Δ-convex mappings