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

Bandar Bin-Mohsin; Muhammad Uzair Awan; Muhammad Zakria Javed; Sadia Talib; Hüseyin Budak; Muhammad Aslam Noor; Khalida Inayat Noor; Bandar Bin-Mohsin; Muhammad Uzair Awan; Muhammad Zakria Javed; Sadia Talib; Hüseyin Budak; Muhammad Aslam Noor; Khalida Inayat Noor

doi:10.3934/math.2023103

AIMS Mathematics

2023, Volume 8, Issue 1: 1995-2017. doi: 10.3934/math.2023103

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Research article

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

1.
Department of Mathematics College of Science King Saud University, Riyadh, Saudi Arabia
2.
Department of Mathematics, Government College University, Faisalabad, Pakistan
3.
Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
4.
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

Received: 10 August 2022 Revised: 19 September 2022 Accepted: 23 September 2022 Published: 26 October 2022
MSC : 26D10, 26D15, 26A51, 05A33

In this article, we introduce the notion of $ _{a}{\bar{T}}_{p,q} $-integrals. Using the definition of $ _{a}{\bar{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.
- convex functions,
- $ _{a}{\bar{T}}_{p,q} $-integral,
- Young's inequality,
- Hölder's inequality,
- Minkowski's inequality,
- Ostrowski's inequality,
- Hermite-Hadamard's inequality
Citation: Bandar Bin-Mohsin, Muhammad Uzair Awan, Muhammad Zakria Javed, Sadia Talib, Hüseyin Budak, Muhammad Aslam Noor, Khalida Inayat Noor. On some classical integral inequalities in the setting of new post quantum integrals[J]. AIMS Mathematics, 2023, 8(1): 1995-2017. doi: 10.3934/math.2023103

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Abstract

In this article, we introduce the notion of $ _{a}{\bar{T}}_{p,q} $-integrals. Using the definition of $ _{a}{\bar{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.

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