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.
Highlights
Mathematicians use convex functions in many fields, such as optimization and advanced analysis
We will define weighted left-side and right-side interval-valued fractional integrals of a function Ῠ according to another function θ (ζ )
We proposed a new definition of weighted interval-valued fractional integrals of a function Ῠ by combining it with another function θ (ζ )
Summary
Mathematicians use convex functions in many fields, such as optimization and advanced analysis. Convex functions offer several unique qualities, such as a unique minimum on an open set if strictly convex. Convex functions have identical qualities even when the spatial dimension is not finite, and as a result, they are instances of functionals in variation methods. In the theory of probability, a convex function obtained through the use of a random variable is constrained above by the expected value. Numerous inequalities are established for convex functions, but the Hermite-Hadamard inequality is the most well-known from the relevant literature. A function Ῠ : [`1 , `2 ] ⊂ R → R is called convex, if for all1 , `2 ∈ I and ζ ∈ [0, 1],
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