Weighted Midpoint Hermite-Hadamard-Fejér Type Inequalities in Fractional Calculus for Harmonically Convex Functions
Humaira Kalsoom, Miguel José Vivas Cortez, Muhammad Amer Latif, Hijaz Ahmad
Abstract
In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities.
Topics & Concepts
MathematicsMidpointConvex functionHadamard transformHermite polynomialsPure mathematicsType (biology)Fractional calculusMathematical analysisRegular polygonGeometryBiologyEcologyMathematical Inequalities and ApplicationsMathematical functions and polynomials