NEW FRACTIONAL INTEGRAL INEQUALITIES FORLR-ℏ-PREINVEX INTERVAL-VALUED FUNCTIONS

Abstract

Based on the pseudo-order relation, we introduce the concept of left and right $\hslash$-preinvex interval-valued functions (LR-$\hslash$-PIVFs). Further, we establish the Hermite–Hadamard and Hermite–Hadamard–Fejér-type estimates for LR-$\hslash$-PIVFs using generalized fractional integrals. Finally, an example of interval-valued fractional integrals is provided to illustrate the validity of the results derived herein. Our results not only extend some existing inequalities for Hadamard, Riemann–Liouville, and Katugampola fractional integrals, but also provide new insights for future research on generalized convexity and IVFs, among others.