Weighted fractional inequalities for new conditions on h-convex functions - Benaissa, Bouharket; Azzouz, Noureddine; Budak, Hüseyin (Boundary value problems, 2024)
We use a new function class called B -function to establish a novel version of Hermite–Hadamard inequality for weighted ψ -Hilfer operators. Additionally, we prove two new identities involving weighted ψ -Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B -function, we derive several trapezoid- and midpoint-type inequalities for h -convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h .