Differences of two semiconvex functions on the real line

Abstract

We give a complete characterization of real functions on the real line which can be represented as the difference of two semiconvex functions with a general modulus (or of two strongly paraconvex functions).

Keywords

• Semiconvex function with general modulus
• difference of two semiconvex functions
• omega-nondecreasing function
• [omega]-variation
• regulated function.