An application of Hayashi's inequality in numerical integration-Reference-Cited by-同舟云学术

An application of Hayashi's inequality in numerical integration

Published:2023-01-01 Issue:1 Volume:21 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Heilat Ahmed Salem¹,Qazza Ahmad²,Hatamleh Raed¹,Saadeh Rania²,Alomari Mohammad W.¹

Affiliation:

1. Department of Mathematics, Faculty of Science and Information Technology, Jadara University , P.O. Box 733 , Irbid 21110 , Jordan

2. Department of Mathematics, Faculty of Science, Zarqa University , Zarga 13110 , Jordan

Abstract

Abstract This study systematically develops error estimates tailored to a specific set of general quadrature rules that exclusively incorporate first derivatives. Moreover, it introduces refined versions of select generalized Ostrowski’s type inequalities, enhancing their applicability. Through the skillful application of Hayashi’s celebrated inequality to specific functions, the provided proofs underpin these advancements. Notably, this approach extends its utility to approximate integrals of real functions with bounded first derivatives. Remarkably, it employs Newton-Cotes and Gauss-Legendre quadrature rules, bypassing the need for stringent requirements on higher-order derivatives.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/math-2023-0162/pdf

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