Set Inclusions of the Hermite-Hadamard Type for $m$ Polynomial Harmonically Convex Interval Valued Functions

Abstract

We introduce the notion of $m$-polynomial harmonically convex interval-valued function. A relationship between a given interval-valued function and its component real-valued functions is pointed out. Moreover, some new Hermite--Hadamard type results are established for this class of functions. Our results complement and extend existing results in the literature. By taking $m\geq 2$, we derive loads of new and interesting inclusions. We anticipate that the idea outlined herein will trigger further investigations in this direction.

Keywords

• Hermite--Hadamard
• $m$-polynomial harmonically convex
• interval-valued function

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