Some new hermite-hadamard-fejér fractional type inequalities for h-convex and harmonically h-convex interval-valued functions

Abstract

In this article, firstly, we establish a novel definition of weighted interval-valued fractional integrals of a function Ῠ 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 Ῠ 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 Ῠ according to another function ϑ(˙ζ). Finally, by using weighted interval-valued fractional integrals of a function Ῠ 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.