Some New Hermite-Hadamard-Fejer 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 Upsilon using an another function & thetasym;(zeta). As an additional observation, it is noted that the new class of weighted interval-valued fractional integrals of a function Upsilon by employing an additional function & thetasym;(zeta) 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-Fejer type inequality for h-convex interval-valued functions using weighted interval-valued fractional integrals of a function Upsilon according to another function & thetasym;(zeta). Finally, by using weighted interval-valued fractional integrals of a function Upsilon according to another function & thetasym;(zeta), we are establishing a new Hermite-Hadamard-Fejer type inequality for harmonically h-convex interval-valued functions that is not previously known. Moreover, some examples are provided to demonstrate our results.