Some Novel Inequalities for Godunova–Levin Preinvex Functions via Interval Set Inclusion ⊆ Relation

Abstract

In this note, we introduce the concept of ℏ-Godunova–Levin interval-valued preinvex functions. As a result of these novel notions, we have developed several variants of Hermite–Hadamard and Fejér-type inequalities under inclusion order relations. Furthermore, we demonstrate through suitable substitutions that this type of convexity unifies a variety of other convex classes. To further support our main findings, we formulated several remarks and nontrivial examples.