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Research Article | Open Access

Some Hermite-Hadamard and midpoint type inequalities in symmetric quantum calculus

Saad Ihsan Butt1Muhammad Nasim Aftab1Hossam A. Nabwey2( )Sina Etemad3,4
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Iraq
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Abstract

The Hermite-Hadamard inequalities are common research topics explored in different dimensions. For any interval [ b 0 , b 1 ] , we construct the idea of the Hermite-Hadamard inequality, its different kinds, and its generalization in symmetric quantum calculus at b 0 [ b 0 , b 1 ] . We also construct parallel results for the Hermite-Hadamard inequality, its different types, and its generalization on other end point b 1 , and provide some examples as well. Some justification with graphical analysis is provided as well. Finally, with the assistance of these outcomes, we give a midpoint type inequality and some of its approximations for convex functions in symmetric quantum calculus.

CLC number: 05A30, 26A51, 26D10, 26D15

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AIMS Mathematics
Pages 5523-5549

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Cite this article:
Butt SI, Aftab MN, Nabwey HA, et al. Some Hermite-Hadamard and midpoint type inequalities in symmetric quantum calculus. AIMS Mathematics, 2024, 9(3): 5523-5549. https://doi.org/10.3934/math.2024268

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Received: 20 November 2023
Revised: 18 January 2024
Accepted: 22 January 2024
Published: 15 March 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)