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, Hölder's and Minkowski's inequalities for the $IR$ $\Delta$-integral. Also, some examples are given to illustrate our theorems.

arXiv commentThis is a preprint of a paper whose final and definite form is with 'Soft Computing', available from [https://link.springer.com/journal/500]. Submitted 20-Dec-2017; Revised 31-Aug-2018; Accepted 11-Sept-2018

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Cited by in corpus (2)

• On the Hermite-Hadmard inequalities for interval-valued coordinated convex functions
• Discrete Opial type inequalities for interval-valued functions