Some perturbed inequalities of Ostrowski type for high-order differentiable functions and applications

Abstract

We firstly establish inequalities for functions whose high degree derivatives are convex via an equality which was presented previously. Then we derive inequalities for functions whose high-order derivatives are absolutely continuous by using the same equality. In addition, we examine connections between inequalities obtained in earlierworks and our results. Finally, some estimates of composite quadrature rules are given.