Lipschitz sums of convex functions

Volume 158 / 2003

Marianna Csörnyei, Assaf Naor Studia Mathematica 158 (2003), 269-286 MSC: 52A41, 26B25. DOI: 10.4064/sm158-3-6


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.


  • Marianna CsörnyeiDepartment of Mathematics
    University College London
    Gower Street
    London, WC1E 6BT, United Kingdom
  • Assaf NaorDepartment of Mathematics
    Hebrew University, Givaat-Ram
    Jerusalem, Israel

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