Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators

Abstract

In this article, the notion of interval-valued preinvex functions involving the Riemann–Liouville fractional integral is described. By applying this, some new refinements of the Hermite–Hadamard inequality for the fractional integral operator are presented. Some novel special cases of the presented results are discussed as well. Also, some examples are presented to validate our results. The established outcomes of our article may open another direction for different types of integral inequalities for fractional interval-valued functions, fuzzy interval-valued functions, and their associated optimization problems.

Enlarged integral inequalities through recent fractional generalized operators

“…Therefore by ( 28), (30), and (31) we get (H c (0) + H c γ g q (t, 0, γ ) λ J γ θ,q γ g q (t, 0, γ )…”

“…Additional generalizations and expansions can be found, for instance, in [21,23,28,30]. Moreover, we can begin by recalling some basic fractional notions.…”

Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities

“…In the future, we will use generalized interval and fuzzy Riemann-Liouville fractional operators to investigate this concept for generalized left and right convex I•V-Fs and F-I•V-Fs by using interval Katugampola fractional integrals and fuzzy Katugampola fractional integrals. For applications, see [53][54][55][56].…”

Hermite–Hadamard type inequality for (E, F)-convex functions and geodesic (E, F)-convex functions

“…Publications [2,7,12,18,23] are recommended for readers interested in generalizations of the Hadamard-type inequality. Now, we present the Hermite-Hadamard-type inequalities for (E, F )-convex as follows:…”