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Research Article | Open Access

Dynamic inequalities of Grüss, Ostrowski and Trapezoid type via diamond- α integrals and Montgomery identity

Marwa M. Tharwat1, Marwa M. Ahmed1, Ammara Nosheen2, Khuram Ali Khan2 ( ), Iram Shahzadi2, Dumitru Baleanu3( ), Ahmed A. El-Deeb4
Electrical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
Lebanese American University, Department of Computer Science and Mathematics, Beirut, Lebanon
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
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Abstract

In this article, the Montgomery identity and Ostrowski inequality are established for univariate first-order diamond-alpha differentiable functions. We also investigate the generalization of Ostrowski-type inequalities for bivariate functions with bounded second-order diamond-alpha derivatives by applying integration by parts for ♢ α -integrals. Moreover, some extensions of dynamic trapezoid- and Grüss-type inequalities are also obtained by using the Montgomery identity.

Keywords

Grüss-type inequalitydiamond-α integralOstrowski inequalitytrapezoid inequalityMontgomery identity
CLC number: 39B62, 39B05, 26D15, 26D20, 26D10

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AIMS Mathematics
Volume 9 Issue 5,
May 2024
Pages 12778-12799
DOI: 10.3934/math.2024624

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Cite this article:
Tharwat MM, Ahmed MM, Nosheen A, et al. Dynamic inequalities of Grüss, Ostrowski and Trapezoid type via diamond- α integrals and Montgomery identity. AIMS Mathematics, 2024, 9(5): 12778-12799. https://doi.org/10.3934/math.2024624

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Received: 25 January 2024
Revised: 13 March 2024
Accepted: 19 March 2024
Published: 15 May 2024
©2024 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)