AIMS Mathematics, 2021, 6(1): 362-377. doi: 10.3934/math.2021022.

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

1 Department of Mathematics, Faculty of Science, Bartin University, Bartin, Turkey
2 Department of Mathematics, Faculty of Science, Gebze Technical University, Kocaeli, Turkey
3 Department of Mathematics, Huzhou University, Huzhou 313000, China
4 Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

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.
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Keywords absolutely continuous function; Ostrowski inequality; Perturbed type inequalities; numerical integration

Citation: Samet Erden, Nuri Çelİk, Muhammad Adil Khan. Refined inequalities of perturbed Ostrowski type for higher-order absolutely continuous functions and applications. AIMS Mathematics, 2021, 6(1): 362-377. doi: 10.3934/math.2021022

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