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

• DOI: 10.3390/math10010074
• Publication Date: 2021-12-27T06:06:54Z
• Authors: Humaira Kalsoom; Muhammad Latif; Zareen Khan; Miguel Vivas-Cortez
• Keywords: weighted interval-valued fractional operators; QA1-939; <i>h</i>-harmonically convex interval-valued functions; 0101 mathematics; 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; weighted interval-valued Hermite-Hadamard type inequality; 01 natural sciences; Mathematics; <i>h</i>-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.