Some inequalities for interval-valued functions on time scales

Abstract

We introduce the interval Darboux delta integral (shortly, the $ID$ $\Delta$-integral) and the interval Riemann delta integral (shortly, the $IR$ $\Delta$-integral) for interval-valued functions on time scales. Fundamental properties of $ID$ and $IR$ $\Delta$-integrals and examples are given. Finally, we prove Jensen's, H\"{o}lder's and Minkowski's inequalities for the $IR$ $\Delta$-integral. Also, some examples are given to illustrate our theorems.