Generalized $ (p, q) $-analogues of Dragomir-Agarwal's inequalities involving Raina's function and applications

Miguel Vivas-Cortez; Muhammad Zakria Javed; Muhammad Uzair Awan; Artion Kashuri; Muhammad Aslam Noor; Miguel Vivas-Cortez; Muhammad Zakria Javed; Muhammad Uzair Awan; Artion Kashuri; Muhammad Aslam Noor

doi:10.3934/math.2022639

AIMS Mathematics

2022, Volume 7, Issue 6: 11464-11486. doi: 10.3934/math.2022639

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Research article

Generalized $ (p, q) $-analogues of Dragomir-Agarwal's inequalities involving Raina's function and applications

1.
Escuela de Ciencias Fsicas y Matemticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Catlica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador
2.
Department of Mathematics, Government College University, Faisalabad, Pakistan
3.
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400 Vlora, Albania
4.
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

Received: 19 January 2022 Revised: 02 March 2022 Accepted: 02 March 2022 Published: 13 April 2022
MSC : 05A30, 26A33, 26A51, 34A08, 26D07, 26D10, 26D15

In this paper, we introduce the class of generalized strongly convex functions using Raina's function. We derive two new general auxiliary results involving first and second order $ (p, q) $-differentiable functions and Raina's function. Essentially using these identities and the generalized strongly convexity property of the functions, we also found corresponding new generalized post-quantum analogues of Dragomir-Agarwal's inequalities. We discuss some special cases about generalized convex functions. To support our main results, we offer applications to special means, to hypergeometric functions, to Mittag-Leffler functions and also to $ (p, q) $-differentiable functions of first and second order that are bounded in absolute value.
- Dragomir-Agarwal's inequality,
- Hölder inequality,
- power-mean inequality,
- generalized strongly convex functions,
- Raina's function,
- post-quantum calculus
Citation: Miguel Vivas-Cortez, Muhammad Zakria Javed, Muhammad Uzair Awan, Artion Kashuri, Muhammad Aslam Noor. Generalized $ (p, q) $-analogues of Dragomir-Agarwal's inequalities involving Raina's function and applications[J]. AIMS Mathematics, 2022, 7(6): 11464-11486. doi: 10.3934/math.2022639

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Abstract

In this paper, we introduce the class of generalized strongly convex functions using Raina's function. We derive two new general auxiliary results involving first and second order $ (p, q) $-differentiable functions and Raina's function. Essentially using these identities and the generalized strongly convexity property of the functions, we also found corresponding new generalized post-quantum analogues of Dragomir-Agarwal's inequalities. We discuss some special cases about generalized convex functions. To support our main results, we offer applications to special means, to hypergeometric functions, to Mittag-Leffler functions and also to $ (p, q) $-differentiable functions of first and second order that are bounded in absolute value.

References

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