“…We say that a function f ∈ C[0, 1] is q-monotone if ∆ q δ (f, x) ≥ 0 for all δ > 0, and denote the set of all q-monotone (continuous) functions by ∆ (q) . In particular, ∆ (0) , ∆ (1) and ∆ (2) are, respectively, the classes of all nonnegative, nondecreasing and convex functions from C[0, 1]. We also remark that, for q ≥ 3, f ∈ C[0, 1] is q-monotone if and only if f ∈ C q−2 (0, 1) and f (q−2) is convex in (0, 1).…”