Modulus of convexity for operator convex functions

Given an operator convex function f(x), we obtain an operator-valued lower bound for cf(x) + (1 - c) f(y) - f(cx + (1 - c) y), c is an element of[0, 1]. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is shown to be false for functions that are convex but not operator convex. (C) 2014 AIP Publishing LLC.