Hermite-Hadamard-Mercer and related inequalities for $h$-convex functions via $\psi$-Hilfer operators

Abstract

We prove a fractional Hermite-Hadamard-Mercer inequality via $\psi $-Hilferintegral operators for the class of $h-$convex functions, where $h$ is a $B$%-function. Some novel fractional inequalities related to the left and rightsides of the Hermite-Hadamard-Mercer inequalities are established fordifferentiable mappings whose absolute values of the derivatives are $h-$%convex. Moreover, we construct new inequalities for these differentiablefunctions using H\"{o}lder's inequality.