Refined inequalities of perturbed Ostrowski type for higher-order absolutely continuous functions and applications

Abstract

First of all, we establish an identity for higher-order differentiable functions. Then, we prove some integral inequalities for mappings that have continuous derivatives up to the order $n-1$ with $n\geq 1$ and whose n-th derivatives are the element of $L_{1},~L_{r}$, and $L_{\infty }.$ In addition, estimates of new composite quadrature rules are examined. Finally, natural applications for exponential and logarithmic functions are given.

Keywords

• absolutely continuous function
• ostrowski inequality
• perturbed type inequalities
• numerical integration