New quantum integral inequalities for left and right log-ℏ-convex interval-valued functions

Abstract

We introduce the concept of quantum integration for interval-valued functions and establish new q-Hermite–Hadamard and q-Hermite–Hadamard–Fejér inequalities for left and right log ⁢ - ⁢ h {\mathrm{log}\text{-}h} -convex interval-valued functions. Our results generalize the known ones in the literature and serve as a foundation for future studies in inequalities for interval-valued functions and interval differential equations. We illustrate our results with examples.