Perturbed Trapezoid Like Inequalities

Waseem Ghazi Alshanti; Iqbal Mohammad Batiha; Ahmad Alshanty; Amjed Zraiqat; Iqbal Hamzah Jebril; Ma’Mon Abu Hammad

doi:10.26554/sti.2023.8.2.205-211

Perturbed Trapezoid Like Inequalities

Waseem Ghazi Alshanti
, Iqbal Mohammad Batiha
, Ahmad Alshanty
, Amjed Zraiqat
, Iqbal Hamzah Jebril
, Ma’Mon Abu Hammad

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
Al-Isra Private University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In our current research article, based on a general configuration of a 3-step Peano kernel, new versions of integral inequality of Ostrowski’s type are developed for differentiable mappings that have second derivatives belong to L_∞. Then we utilized these versions to generate new perturbed trapezoid like inequalities. These new perturbed trapezoid like inequalities are proposed with error bounds smaller than and similar to those reported by previous studies. Moreover, some of the obtained perturbed trapezoid like inequalities reveal the relationship between the Euler-Maclaurin summation and the trapezoidal rule. Finally, certain implementations to numerical composite quadrature rules are provided for completeness.

Original language	English
Pages (from-to)	205-211
Number of pages	7
Journal	Science and Technology Indonesia
Volume	8
Issue number	2
DOIs	https://doi.org/10.26554/sti.2023.8.2.205-211
State	Published - Apr 2023

Keywords

Euler-Maclaurin Summation Formula
Ostrowski Inequality
Perturbed Trapezoid Type Inequality

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10.26554/sti.2023.8.2.205-211

Cite this

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title = "Perturbed Trapezoid Like Inequalities",

abstract = "In our current research article, based on a general configuration of a 3-step Peano kernel, new versions of integral inequality of Ostrowski{\textquoteright}s type are developed for differentiable mappings that have second derivatives belong to L∞. Then we utilized these versions to generate new perturbed trapezoid like inequalities. These new perturbed trapezoid like inequalities are proposed with error bounds smaller than and similar to those reported by previous studies. Moreover, some of the obtained perturbed trapezoid like inequalities reveal the relationship between the Euler-Maclaurin summation and the trapezoidal rule. Finally, certain implementations to numerical composite quadrature rules are provided for completeness.",

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AU - Alshanti, Waseem Ghazi

AU - Batiha, Iqbal Mohammad

AU - Alshanty, Ahmad

AU - Zraiqat, Amjed

AU - Jebril, Iqbal Hamzah

AU - Hammad, Ma’Mon Abu

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AB - In our current research article, based on a general configuration of a 3-step Peano kernel, new versions of integral inequality of Ostrowski’s type are developed for differentiable mappings that have second derivatives belong to L∞. Then we utilized these versions to generate new perturbed trapezoid like inequalities. These new perturbed trapezoid like inequalities are proposed with error bounds smaller than and similar to those reported by previous studies. Moreover, some of the obtained perturbed trapezoid like inequalities reveal the relationship between the Euler-Maclaurin summation and the trapezoidal rule. Finally, certain implementations to numerical composite quadrature rules are provided for completeness.

KW - Euler-Maclaurin Summation Formula

KW - Ostrowski Inequality

KW - Perturbed Trapezoid Type Inequality

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VL - 8

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JO - Science and Technology Indonesia

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Perturbed Trapezoid Like Inequalities

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Keywords

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