Some New Generalized Inequalities of Hardy Type Involving Several Functions on Time Scale Nabla Calculus

In this article, we establish several new generalized Hardy-type inequalities involving several functions on time-scale nabla calculus. Furthermore, we derive some new multidimensional Hardy-type inequalities on time scales nabla calculus. The main results are proved by applying Minkowski’s inequali...

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Bibliographic Details
Published in:Axioms 2022-12, Vol.11 (12), p.662
Main Authors: Saied, A. I., ALNemer, Ghada, Zakarya, Mohammed, Cesarano, Clemente, Rezk, Haytham M.
Format: Article
Language:English
Subjects:
arithmetic mean–geometric mean inequality
Calculus
Hardy-type inequality
Inequalities
Inequalities (Mathematics)
Mathematical analysis
Mathematical research
time scales nabla calculus
weighted functions
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Summary:In this article, we establish several new generalized Hardy-type inequalities involving several functions on time-scale nabla calculus. Furthermore, we derive some new multidimensional Hardy-type inequalities on time scales nabla calculus. The main results are proved by applying Minkowski’s inequality, Jensen’s inequality and Arithmetic Mean–Geometric Mean inequality. As a special case of our results, when T=R, we obtain refinements of some well-known continuous inequalities and when T=N, the results which are essentially new.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms11120662