Quantum Hermite-Hadamard type inequalities for generalized strongly preinvex functions

Humaira Kalsoom; Muhammad Amer Latif; Muhammad Idrees; Muhammad Arif; Zabidin Salleh; Humaira Kalsoom; Muhammad Amer Latif; Muhammad Idrees; Muhammad Arif; Zabidin Salleh

doi:10.3934/math.2021769

AIMS Mathematics

2021, Volume 6, Issue 12: 13291-13310. doi: 10.3934/math.2021769

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Quantum Hermite-Hadamard type inequalities for generalized strongly preinvex functions

1.
Department of Mathematical, Zhejiang Normal University, Jinhua 321004, China
2.
Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia
3.
Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
4.
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
5.
Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia

Received: 20 March 2021 Accepted: 07 September 2021 Published: 16 September 2021
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

In accordance with the quantum calculus, the quantum Hermite-Hadamard type inequalities shown in recent findings provide improvements to quantum Hermite-Hadamard type inequalities. We acquire a new $ q{_{\kappa_1}} $-integral and $ q{^{\kappa_2}} $-integral identities, then employing these identities, we establish new quantum Hermite-Hadamard $ q{_{\kappa_1}} $-integral and $ q{^{\kappa_2}} $-integral type inequalities through generalized higher-order strongly preinvex and quasi-preinvex functions. The claim of our study has been graphically supported, and some special cases are provided as well. Finally, we present a comprehensive application of the newly obtained key results. Our outcomes from these new generalizations can be applied to evaluate several mathematical problems relating to applications in the real world. These new results are significant for improving integrated symmetrical function approximations or functions of some symmetry degree.
Citation: Humaira Kalsoom, Muhammad Amer Latif, Muhammad Idrees, Muhammad Arif, Zabidin Salleh. Quantum Hermite-Hadamard type inequalities for generalized strongly preinvex functions[J]. AIMS Mathematics, 2021, 6(12): 13291-13310. doi: 10.3934/math.2021769

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Abstract

In accordance with the quantum calculus, the quantum Hermite-Hadamard type inequalities shown in recent findings provide improvements to quantum Hermite-Hadamard type inequalities. We acquire a new $ q{_{\kappa_1}} $-integral and $ q{^{\kappa_2}} $-integral identities, then employing these identities, we establish new quantum Hermite-Hadamard $ q{_{\kappa_1}} $-integral and $ q{^{\kappa_2}} $-integral type inequalities through generalized higher-order strongly preinvex and quasi-preinvex functions. The claim of our study has been graphically supported, and some special cases are provided as well. Finally, we present a comprehensive application of the newly obtained key results. Our outcomes from these new generalizations can be applied to evaluate several mathematical problems relating to applications in the real world. These new results are significant for improving integrated symmetrical function approximations or functions of some symmetry degree.

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