Characterization of convex functions
Volume 192 / 2009
Studia Mathematica 192 (2009), 29-37
MSC: 26B25, 39B62.
DOI: 10.4064/sm192-1-3
Abstract
There are many inequalities which in the class of continuous functions are equivalent to convexity (for example the Jensen inequality and the Hermite–Hadamard inequalities). We show that this is not a coincidence: every nontrivial linear inequality which is valid for all convex functions is valid only for convex functions.
