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 Δ-convex functions.
Original language | English (US) |
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Pages (from-to) | 269-286 |
Number of pages | 18 |
Journal | Studia Mathematica |
Volume | 158 |
Issue number | 3 |
DOIs | |
State | Published - 2003 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Convex functions
- Lipschitz functions
- Δ-convex mappings