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Journals / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 1

Diamond alpha Hardy-Copson type dynamic inequalities

Zeynep KAYAR
Billur KAYMAKÇALAN
Pages
48–73
Publication Date
2022-02-14
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals.
📊
Key Findings & Data:The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together.
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Conclusion & Impact:Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Diamond alpha calculus · Hardy’s inequality · Copson’s inequality

Abstract

In this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals. The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together. The second kind involves another twelve new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Hardy-Copson type inequalities. Our approach is quite new due to the fact that it uses time scale calculus rather than algebra. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.

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Cite This Article

KAYAR, Z., KAYMAKÇALAN, B. (2022). Diamond alpha Hardy-Copson type dynamic inequalities. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 1, 48–73. https://ajindex.com/articles/669238

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