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Research Article | Open Access

Weighted Ostrowski type inequalities via Montgomery identity involving double integrals on time scales

Atiqe Ur Rahman1,†, Khuram Ali Khan2, Ammara Nosheen2, Muhammad Saeed1, Thongchai Botmart3( ), Nehad Ali Shah4,†
Department of Mathematics, University of Management and Technology, Lahore 54000, Pakistan
Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Department of Mechanical Engineering, Sejong University, Seoul 05006, South Korea

† These authors contributed equally to this work and are co-first authors

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Abstract

In this paper, the Montgomery identity is generalized for double integrals on time scales by employing a novel analytical approach to develop the generalized Ostrowski type integral inequalities involving double integrals. Some inimitable cases are discussed for different parameters and parametric functions. Moreover, applications to some particular time scales are also presented.

Keywords

Ostrowski inequalitiesMontgomery identitytime scalespolynomials
CLC number: 26D07, 26D15, 26E70

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16657-16672
DOI: 10.3934/math.2022913

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Cite this article:
Rahman AU, Khan KA, Nosheen A, et al. Weighted Ostrowski type inequalities via Montgomery identity involving double integrals on time scales. AIMS Mathematics, 2022, 7(9): 16657-16672. https://doi.org/10.3934/math.2022913

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Received: 17 March 2022
Revised: 28 June 2022
Accepted: 29 June 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)