Some inequalities for interval-valued functions on time scales View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-09-27

AUTHORS

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

ABSTRACT

We introduce the interval Darboux delta integral (shortly, the IDΔ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ID}\,\varDelta $$\end{document}-integral) and the interval Riemann delta integral (shortly, the IR Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta $$\end{document}-integral) for interval-valued functions on time scales. Fundamental properties of ID\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ID}$$\end{document} and IR Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta $$\end{document}-integrals and examples are given. Finally, we prove Jensen’s, Hölder’s and Minkowski’s inequalities for the IR Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta $$\end{document}-integral. Also, some examples are given to illustrate our theorems. More... »

PAGES

6005-6015

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00500-018-3538-6

DOI

http://dx.doi.org/10.1007/s00500-018-3538-6

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https://app.dimensions.ai/details/publication/pub.1107273144


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