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New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization

Saeed Tareq, Khan Muhammad Adil, Faisal Shah, Alsulami Hamed H., Alhodaly Mohammed Sh.

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220225

The Hermite-Hadamard inequality is regarded as one of the most favorable inequalities from the research point of view. Currently, mathematicians are working on extending, improving, and generalizing this inequality. This article presents conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in weighted and unweighted forms by using the idea of majorization and convexity together with generalized conformable fractional integral operators. They not only represent continuous and discrete inequalities in compact form but also produce generalized inequalities connecting various fractional operators such as Hadamard, Katugampola, Riemann-Liouville, conformable, and Rieman integrals into one single form. Also, two new integral identities have been investigated pertaining a differentiable function and three tuples. By using these identities and assuming ∣f'∣ and ∣f'∣q(q>1) as convex, we deduce bounds concerning the discrepancy of the terms of the main inequalities.