English

Some inequalities for interval-valued functions on time scales

Classical Analysis and ODEs 2019-07-05 v1

Abstract

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

Keywords

Cite

@article{arxiv.1809.03709,
  title  = {Some inequalities for interval-valued functions on time scales},
  author = {Dafang Zhao and Guoju Ye and Wei Liu and Delfim F. M. Torres},
  journal= {arXiv preprint arXiv:1809.03709},
  year   = {2019}
}

Comments

This 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

R2 v1 2026-06-23T04:01:54.468Z