Some New Dynamic Inequalities Involving The Dyanamic Hardy Operator With Kernels

Authors

Doaa M. Abdou, Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Nasr City 11884, Cairo, EgyptFollow
Haytham M. Rezk, Department of Mathematics, Faculty of Science (Boys), Al-Azhar University, Nasr City 11884, Cairo, Egypt
Afaf S. Zaghrout, Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Nasr City 11884, Cairo, Egypt
Samir H. Saker, Department of Mathematics, Faculty of Science, New Mansoura University, New Mansoura City, Egypt

Document Type

Original Article

Subject Areas

Mathematics and Statistics

Keywords

Hardy's inequality, Hardy's operator, Hardy-Hilbert's inequality, Jensen's functional, Jensen's inequality, Time scales

Abstract

In this article, by using dynamic Jensen’s inequality and its reverse, we prove some forms of dynamic inequalities involving the dynamic Hardy’s operator. As special cases of our results, we obtain refinements of some well-known Hardy-type inequalities and Hardy-Hilbert’s inequality for double integrals. Our findings are the generalization of some results in the literature.

How to Cite This Article

Abdou, Doaa M.; Rezk, Haytham M.; Zaghrout, Afaf S.; and Saker, Samir H. (2024) "Some New Dynamic Inequalities Involving The Dyanamic Hardy Operator With Kernels," Al-Azhar Bulletin of Science: Vol. 35: Iss. 2, Article 9.
DOI: https://doi.org/10.58675/2636-3305.1680