Hermite-Hadamard-Type Fractional Inclusions for Interval-Valued Preinvex Functions

Abstract

We introduce a new class of interval-valued preinvex functions termed as harmonically h-preinvex interval-valued functions. We establish new inclusion of Hermite–Hadamard for harmonically h-preinvex interval-valued function via interval-valued Riemann–Liouville fractional integrals. Further, we prove fractional Hermite–Hadamard-type inclusions for the product of two harmonically h-preinvex interval-valued functions. In this way, these findings include several well-known results and newly obtained results of the existing literature as special cases. Moreover, applications of the main results are demonstrated by presenting some examples.

Keywords

• Hermite–Hadamard inequalities
• harmonical convex functions
• interval-valued functions
• fractional integrals