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arXiv · 1809.03709

Some inequalities for interval-valued functions on time scales

Dafang Zhao·Guoju Ye·Wei Liu·Delfim F. M. Torres
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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.

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Dafang Zhao, Guoju Ye, Wei Liu, Delfim F. M. Torres. 2018-09-11. Some inequalities for interval-valued functions on time scales. https://doi.org/10.1007/s00500-018-3538-6

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