A STUDY OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS
- 18 January 2024
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in Fractals
- Vol. 32 (02)
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.Keywords
Funding Information
- Human Resources and Institutional Development, Research, and Innovation (B05F640163)
- Pontifical Catholic University of Ecuador Project (070-UIO-2022)
This publication has 16 references indexed in Scilit:
- On New Estimates of q-Hermite–Hadamard Inequalities with Applications in Quantum CalculusAxioms, 2023
- A new version of $( p,q ) $-Hermite–Hadamard’s midpoint and trapezoidal inequalities via special operators in $( p,q ) $-calculusBoundary Value Problems, 2022
- New Hermite–Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of FunctionsMathematics, 2022
- On Some New Ostrowski–Mercer-Type Inequalities for Differentiable FunctionsAxioms, 2022
- Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Convex FunctionFractal and Fractional, 2021
- Some New Results on Hermite–Hadamard–Mercer-Type Inequalities Using a General Family of Fractional Integral OperatorsFractal and Fractional, 2021
- Hermite-Hadamard-Mercer type inequalities for fractional integralsFilomat, 2021
- New fractional estimates for Hermite-Hadamard-Mercer’s type inequalitiesAlexandria Engineering Journal, 2020
- Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalitiesMathematical and Computer Modelling, 2013
- On new inequalities of Simpson’s type for-convex functionsComputers & Mathematics with Applications, 2010