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 - 1 and whose n-th derivatives are the element of L-1, L-r, and L-infinity. In addition, estimates of new composite quadrature rules are examined. Finally, natural applications for exponential and logarithmic functions are given.