Some New Hermite-Hadamard-Fejér Fractional Type Inequalities for h -Convex and Harmonically h -Convex Interval-Valued Functions

In this article, firstly, we establish a novel definition of weighted interval-valued fractional integrals of a function Υ ˘ using an another function ϑ ( ζ ˙ ) . As an additional observation, it is noted that the new class of weighted interval-valued fractional integrals of a function Υ ˘ by employing an additional function ϑ ( ζ ˙ ) characterizes a variety of new classes as special cases, which is a generalization of the previous class. Secondly, we prove a new version of the Hermite-Hadamard-Fejér type inequality for h -convex interval-valued functions using weighted interval-valued fractional integrals of a function Υ ˘ according to another function ϑ ( ζ ˙ ) . Finally, by using weighted interval-valued fractional integrals of a function Υ ˘ according to another function ϑ ( ζ ˙ ) , we are establishing a new Hermite-Hadamard-Fejér type inequality for harmonically h -convex interval-valued functions that is not previously known. Moreover, some examples are provided to demonstrate our results.