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Journals / Turkish Journal of Mathematics / 2021 / Cilt: 45 - Sayı: 2

Hardy–Copson type inequalities for nabla time scale calculus

Billur KAYMAKÇALAN
Zeynep KAYAR
Pages
1040–1064
Publication Date
2022-11-01
DOI
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AI Summary & Key Takeaways

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

Moreover, these dynamic inequalities not only generalize and unify the relatedones in the literature but also improve them in the special cases.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper is devoted to the nabla unification of the discrete and continuous Hardy–Copson type inequalities.Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for thediscrete, continuous, and delta cases.
📊
Key Findings & Data:This paper is devoted to the nabla unification of the discrete and continuous Hardy–Copson type inequalities.Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for thediscrete, continuous, and delta cases.
💡
Conclusion & Impact:Moreover, these dynamic inequalities not only generalize and unify the relatedones in the literature but also improve them in the special cases.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This paper is devoted to the nabla unification of the discrete and continuous Hardy–Copson type inequalities.Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for thediscrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the relatedones in the literature but also improve them in the special cases.

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Cite This Article

KAYMAKÇALAN, B., KAYAR, Z. (2022). Hardy–Copson type inequalities for nabla time scale calculus. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 2, 1040–1064. https://ajindex.com/articles/607381

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References (18)

  1. Agarwal RP, Bohner M, Peterson A. Inequalities on time scales: A survey. Mathematical Inequalities & Applications 2001; 4 (4): 535-557
  2. Agarwal RP, O’Regan D, Saker S. Dynamic Inequalities On Time Scales. Switzerland: Springer International Publishing, 2014
  3. Agarwal RP, O’Regan D, Saker S. Hardy Type Inequalities on Time Scales. Switzerland: Springer International Publishing, 2016
  4. Agarwal RP, Mahmoud RR, Saker S, Tunç C. New generalizations of Németh-Mohapatra type inequalities on time scales. Acta Mathematica Hungarica 2017; 152 (2): 383-403
  5. Anastassiou GA. Foundations of nabla fractional calculus on time scales and inequalities. Computers and Mathematics with Applications 2010; 59: 3750-3762
  6. Atici FM, Guseinov GSh. On Green’s functions and positive solutions for boundary value problems on time scales. Journal of Computational and Applied Mathematics 2002; 141: 75-99
  7. Balinsky AA, Evans WD, Lewis RT. The Analysis and Geometry of Hardy’s Inequality. Switzerland: Springer International Publishing, 2015
  8. Beesack PR. Hardy’s inequality and its extensions. Pacific Journal of Mathematics 1961; 11: 39-61
  9. Bennett G. Some elementary inequalities. Quarterly Journal of Mathematics 1987; 38 (4): 401-425
  10. Bohner M, Peterson A. Dynamic Equations on Times Scales: An Introduction with Applications. Boston, MA, USA: Springer Science+Business Media New York, 2001
  11. Bohner M, Mahmoud R, Saker SH. Discrete, continuous, delta, nabla, and diamond-alpha Opial inequalities. Mathematical Inequalities & Applications 2015; 18 (3): 923-940
  12. Caputo MC. Time scales: From nabla calculus to delta calculus and vice versa via duality. International Journal of Difference Equations 2010; 5 (1): 25–40
  13. Chu YM, Xu Q, Zhang XM. A note on Hardy’s inequality. Journal of Inequalities and Applications 2014; 2014 (271): 1-10
  14. Copson ET. Note on series of positive terms. Journal of the London Mathematical Society 1928; 3: 49-51
  15. Copson ET. Some integral inequalities. Proceedings of the Royal Society of Edinburgh Section A 1976; 75 (2): 157-164
  16. Güvenilir, AF, Kaymakçalan B, Pelen NN. Constantin’s inequality for nabla and diamond-alpha derivative. Journal of Inequalities and Applications 2015; 2015 (167): 1-17
  17. Hardy GH. Notes on a theorem of Hilbert. Mathematische Zeitschrift 1920; 6 (3-4): 314-317
  18. Hardy GH. Notes on some points in the integral calculus, LX. An inequality between integrals. Messenger of Mathematics