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Discontinuity, Nonlinearity, and Complexity 13(4) (2024) 663--674 | DOI:10.5890/DNC.2024.12.007

Savita Panwar$^1$, Rupakshi Mishra Pandey$^1$, Prakriti Rai$^2$, Sunil Dutt Purohit$^3$, D.L. Suthar$^4$

$^1$ Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida, India

$^2$ Siddharth University, Kapilvastu, Uttar Pradesh India

$^3$ Department of HEAS(Mathematices), Rajasthan Technical University, Kota, India

$^4$ Department of Mathematics, Wollo University, P.O. Box 1145, Dessie, Ethiopia

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Abstract

In this article, we present a novel variant of Hermite-Hadamard-Mercer's inequality for strongly convex functions via ABK-fractional integrals and the Jensen-Mercer's inequality. Further, we introduce some Hermite-Hadamard-Mercer's type inequalities for differentiable functions whose absolute value of the derivative is convex. Some fundamental inequalities, like Holder's inequality and Young's inequality, have been used to establish inequalities. Furthermore, we discuss special cases for our main results and obtain the new Hermite-Hadamard-Mercer's inequalities for convex functions using the ABK-fractional Integral Operator. Additionally, some applications for special means are also given.

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