On interval-valued $\mathbb{K}$-Riemann integral and Hermite-Hadamard type inequalities

Abstract

We introduce the concepts of $\mathbb{K}$-Riemann integral and radial $\mathbb{K}$-g$H$-derivative for interval-valued functions. We also give some important properties of interval-valued $\mathbb{K}$-Riemann integral, and extend interval-valued Hermite-Hadamard type inequalities in the case of $\mathbb{K}$-Riemann integral. Several examples are shown to illustrate the results.

Keywords

• interval-valued functions
• radial $\mathbb{k}$-g$h$-derivative
• $\mathbb{k}$-riemann integral
• hermite-hadamard type inequalities