Properties of the modulus of continuity for monotonous convex functions and applications (Q1895265)

In an earlier paper the author [Calcolo 27, No. 2/3, 195-202 (1990; Zbl 0743.41019)] gave exact calculations of the modulus of continuity \(\omega (f; h)\) for a monotone convex function \(f\in C[a, b]\). Here he proves that \(\omega (f; h)\) is concave on \([a, b]\) as a function of \(h\). As corollaries to his results he obtains some modifications and improvements on some classical results on approximations.