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.

New Hermite–Hadamard Type Inequalities in Connection with Interval-Valued Generalized Harmonically (h1,h2)-Godunova–Levin Functions

“…It was also utilized to support the H − H-and Fejér-type inequalities for the n-polynomial convex interval-valued function [26] and preinvex function [27,28]. Interval-valued coordinated preinvex functions are a recent extension of the interval-valued preinvex function notion introduced by Lai et al [29]. Combined with interval analysis, the H − H inequality was extended to interval h-convex functions in [30], to interval harmonic h-convex functions in [31], to interval (h 1 , h 2 )-convex functions in [32] and to interval harmonically (h 1 , h 2 )-convex functions in [33].…”

Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions

“…Set et al [40] used Raina's fractional integral operators to create new Hermite-Hadamard-Mercer inequalities. With a modified Mittag-Leffler kernel, Srivastava et al [41] created the generalized left-side and right-side fractional integral operators, and they then used this large family of fractional integral operators to study the fascinating Chebyshev inequality. Sun established certain Hermite-Hadamard-type inequalities for extended h-convex functions and modified preinvex functions in refs.…”