Weighted Midpoint Hermite-Hadamard-Fejer Type Inequalities in Fractional Calculus for Harmonically Convex Functions

In this paper, we establish a new version of Hermite-Hadamard-Fejer type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejer 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.

Automated summary

In this paper, a new version of Hermite-Hadamard-Fejer type inequality for harmonically convex functions in the form of weighted fractional integral is established. Integral identities and weighted midpoint fractional Hermite-Hadamard-Fejer type integral inequalities for harmonically convex functions have been obtained by involving positive weighted symmetric functions. These inequalities generalize several well-known inequalities, including classical and Riemann-Liouville fractional integral inequalities.