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

Abstract

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.

Keywords

• weighted interval-valued fractional operators
• <i>h</i>-convex interval-valued functions
• <i>h</i>-harmonically convex interval-valued functions
• weighted interval-valued Hermite-Hadamard type inequality