Inequalities of Hardy-type for Multiple Integrals on Time Scales

Dawood Ahmad\(^a\), Khuram Ali Khan\(^b\), Ammara Nosheen\(^{a,*}\)
\(^a\)Department of Mathematics & Statistics, The University of Lahore, Sargoha Sub-Campus, Sargodha, Pakistan.
\(^b\)Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
Correspondence should be addressed to: Ammara Nosheen at hammaran@gmail.com

Copyright © 2021 Dawood Ahmad, Khuram Ali Khan, Ammara Nosheen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 3 April 2020; Accepted: 17 May 2020; Published Online: 18 May 2021.

Abstract

We extend some inequalities of Hardy-type on time scales for functions depending on more than one parameter. The results are proved by using induction principle, properties of integrals on time scales, chain rules for composition of two functions, Hölder’s inequality and Fubini’s theorem in time scales settings.

Keywords:

Time scales, induction principle, Hardy-type inequalities.