A STUDY OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS
Thanin Sitthiwirattham, Miguel José Vivas Cortez, Muhammad Aamir Ali, Hüseyin Budak, İbrahim Avcı
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.
Topics & Concepts
Differentiable functionHadamard transformMathematicsHermite polynomialsApplied mathematicsFractional calculusPure mathematicsMathematical analysisMathematical Inequalities and ApplicationsMathematical functions and polynomialsMulti-Criteria Decision Making