Fejér–Pachpatte–Mercer-Type Inequalities for Harmonically Convex Functions Involving Exponential Function in Kernel
Saad Ihsan Butt, Saba Yousaf, Khuram Ali Khan, Rostin Mabela Makengo Matendo, Abdullah M. Alsharif
Abstract
In the present study, fractional variants of Hermite–Hadamard, Hermite–Hadamard–Fejér, and Pachpatte inequalities are studied by employing Mercer concept. Firstly, new Hermite–Hadamard–Mercer-type inequalities are presented for harmonically convex functions involving fractional integral operators with exponential kernel. Then, weighted Hadamard–Fejér–Mercer-type inequalities involving exponential function as kernel are proved. Finally, Pachpatte–Mercer-type inequalities for products of harmonically convex functions via fractional integral operators with exponential kernel are constructed.
Topics & Concepts
MathematicsHadamard transformHermite polynomialsConvex functionKernel (algebra)Exponential typeExponential functionType (biology)Pure mathematicsFunction (biology)Regular polygonApplied mathematicsMathematical analysisEvolutionary biologyBiologyGeometryEcologyMathematical Inequalities and ApplicationsMathematical functions and polynomials