Bounds for generalizations of Steffensen’s inequality using Taylor’s formula

Abstract

In this paper, we generalize the identities related to Steffensen’s inequality using the Taylor formula by introducing a positive weight. For these generalized identities, we obtain bounds by applying the weighted Hermite–Hadamard inequality for a convex or concave function of the form $|f^{(n)}{|}^q$. Furthermore, we generalize known weighted Hermite–Hadamard-type inequalities by using new identities associated with Steffensen’s inequality.