A STUDY of FRACTIONAL HERMITE-HADAMARD-MERCER INEQUALITIES for DIFFERENTIABLE FUNCTIONS

Thanin Sitthiwirattham; Miguel Vivas-Cortez; Muhammad Aamir Ali; Hüseyin Budak; Ibrahim Avci

doi:10.1142/S0218348X24400164

A STUDY of FRACTIONAL HERMITE-HADAMARD-MERCER INEQUALITIES for DIFFERENTIABLE FUNCTIONS

Thanin Sitthiwirattham, Miguel Vivas-Cortez^*, Muhammad Aamir Ali, Hüseyin Budak, Ibrahim Avci

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite-Hadamard-Mercer-type inequalities for differentiable function. The main benefit of the newly established inequalities is that these inequalities can be converted into some new Mercer inequalities of midpoint type, trapezoidal type, and Simpson's type for differentiable functions. Finally, we show the validation of the results with the help of some mathematical examples and their graphs.

Original language	English
Article number	2440016
Journal	Fractals
Volume	32
Issue number	2
DOIs	https://doi.org/10.1142/S0218348X24400164
State	Published - 18 Jan 2024

Bibliographical note

Publisher Copyright:
© The Author(s)

Funding

This research has received funding support from the NSRF via the Program Management Unit for Human Resources and Institutional Development, Research, and Innovation (Grant No. B05F640163). This study was also supported via funding from the Pontifical Catholic University of Ecuador Project No. (070-UIO-2022). All the authors would like to thank dear reviewers for their useful and constructive comments to improve the quality of the paper.

Funders	Funder number
NSRF	B05F640163
Pontifical Catholic University of Ecuador	070-UIO-2022

Keywords

Jensen-Mercer Inequality
Midpoint Inequalities
Simpson's Inequalities
Trapezoidal Inequalities

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AB - In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite-Hadamard-Mercer-type inequalities for differentiable function. The main benefit of the newly established inequalities is that these inequalities can be converted into some new Mercer inequalities of midpoint type, trapezoidal type, and Simpson's type for differentiable functions. Finally, we show the validation of the results with the help of some mathematical examples and their graphs.

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KW - Trapezoidal Inequalities

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A STUDY of FRACTIONAL HERMITE-HADAMARD-MERCER INEQUALITIES for DIFFERENTIABLE FUNCTIONS

Abstract

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Keywords

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