Harmonic conformable refinements of Hermite-Hadamard Mercer inequalities by support line and related applications

ABSTRACT

We establish new conformable fractional Hermite-Hadamard (H–H) Mercer type inequalities for harmonically convex functions using the concept of support line. We introduce two new conformable fractional auxiliary equalities in the Mercer sense and apply them to differentiable functions with harmonic convexity. We also use Power-mean, Hölder’s and improved Hölder inequality to derive new Mercer type inequalities via conformable fractional integrals. The accuracy and superiority of the offered technique are clearly depicted through impactful visual illustrations. We also use our technique to derive new estimates for hypergeometric functions and special means of real numbers that are more precise than existing ones. Some applications are provided as well. Our results generalize and extend some existing ones in the literature.

KEYWORDS:

• Harmonic Convex functions
• Jensen Mercer Inequalities
• Fractional Calculus
• Improved Holder type inequalities
• Quadrature Estimations

Acknowledgments

This study was supported via funding from the Pontifical Catholic University of Ecuador Project No. (070-UIO-2022).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the Pontificia Universidad Católica del Ecuador [Project No. 070-UIO-2022].