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Research Article | Open Access

On some classical integral inequalities in the setting of new post quantum integrals

Bandar Bin-Mohsin1, Muhammad Uzair Awan2( ), Muhammad Zakria Javed2, Sadia Talib2, Hüseyin Budak3, Muhammad Aslam Noor4, Khalida Inayat Noor4
Department of Mathematics College of Science King Saud University, Riyadh, Saudi Arabia
Department of Mathematics, Government College University, Faisalabad, Pakistan
Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
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Abstract

In this article, we introduce the notion of a T ¯ p , q -integrals. Using the definition of a T ¯ p , q -integrals, we derive some new post quantum analogues of some classical results of Young's inequality, Hölder's inequality, Minkowski's inequality, Ostrowski's inequality and Hermite-Hadamard's inequality.

Keywords

convex functionsaT¯p, q-integralYoung's inequalityHölder's inequalityMinkowski's inequalityOstrowski's inequalityHermite-Hadamard's inequality
CLC number: 26D10, 26D15, 26A51, 05A33

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AIMS Mathematics
Volume 8 Issue 1,
January 2023
Pages 1995-2017
DOI: 10.3934/math.2023103

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Cite this article:
Bin-Mohsin B, Awan MU, Javed MZ, et al. On some classical integral inequalities in the setting of new post quantum integrals. AIMS Mathematics, 2023, 8(1): 1995-2017. https://doi.org/10.3934/math.2023103

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Received: 10 August 2022
Revised: 19 September 2022
Accepted: 23 September 2022
Published: 15 January 2023
©2023 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)