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AIMS Mathematics

2021, Volume 6, Issue 1: 362-377. doi: 10.3934/math.2021022
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Research article

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
  • Received: 26 May 2020 Accepted: 22 September 2020 Published: 13 October 2020

  • MSC : 26D15, 26A46, 26D10

  • 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.

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

    Related Papers:

  • 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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