Refined inequalities of perturbed Ostrowski type for higher-order absolutely continuous functions and applications - Samet Erden; Nuri Çelİk; Muhammad Adil Khan (AIMS Mathematics, 2021)
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 $L_{∞ }.$ In addition, estimates of new composite quadrature rules are examined. Finally, natural applications for exponential and logarithmic functions are given.