Copson-type Inequalities via the k-Hadamard Operator

Benaissa, Bouharket; Azzouz, Noureddine

doi:10.2478/awutm-2024-0005

Abstract

In this paper, we present a novel class of Copson-type inequalities involving the right-sided k-Hadamard fractional integral operator with all parameters of integrability p ≠ 0 and obtain some classical special cases of Copson inequalities. The main results will be proved by employing the Hölder inequality and the Fubini theorem.

References

B. Benaissa, On some Copson-type integral inequality, Korean. J. Math. 29 (3) (2021), 467-472.
Search in Google Scholar Back to article
E. T. Copson, Note on series of positive terms, J. Lond. Math. Soc. 3 (1928), 49-51.
Search in Google Scholar Back to article
E. T. Copson, Some Integral Inequalities, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 75 (2) (1976), 157-164.
Search in Google Scholar Back to article
A. A. El-Deeb, S. D. Makharesh, J. Awrejcewicz, R. P. Agarwal, Dynamic Hardy-Copson Type Inequalities via (g, a)-Nabla Conformable Derivatives on Time Scales, Symmetry 14 (9) (2022), 1847.
Search in Google Scholar Back to article
P. Gao, H. Zhao, On Copson’s inequalities for 0 < p < 1, J. Inequal. Appl. Volume 2020 (2020), 72.
Search in Google Scholar Back to article
G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities, 2nd edn. Cambridge University Press, Cambridge, 1952.
Search in Google Scholar Back to article
E. Hewitt, K. Stromberg, Real and Abstract Analysis. A Modern Treatment of the Theory of Functions of a Real Variable, second printing corrected, Springer-Verlag, Berlin, 1969.
Search in Google Scholar Back to article
Z. Kayar, B. Kaymakçalan, Hardy-Copson type inequalities for nabla time scale calculus, Turk. J. Math. 45 (2021), 1040-1064.
Search in Google Scholar Back to article
Z. Kayar, B. Kaymakçalan, Some Extended Nabla and Delta Hardy-Copson Type Inequalities with Applications in Oscillation Theory, Bull. Iran. Math. Soc. 48 (2022), 2407-2439.
Search in Google Scholar Back to article
Z. Kayar, B. Kaymakçalan, Diamond alpha Hardy-Copson type dynamic inequalities, Hacettepe J. Math. Stat. 51 (2022), 48-73.
Search in Google Scholar Back to article
C. Niculescu, L. E. Persson, Convex functions and their applications, Vol. 23. New York: Springer, 2006.
Search in Google Scholar Back to article
S. Saker, M. R. Kenawy, Copson and Converses Copson Type Inequalities Via Conformable Calculus, Progr. Fract. Di er. Appl. 5 (3) (2019), 243-254.
Search in Google Scholar Back to article
S. H. Saker, D. O’Regan, R. P. Agarwal, Generalized Hardy, Copson, Leindler and Bennett inequalities on time scales, Math. Nachr. 287 (2014), 686-698.
Search in Google Scholar Back to article
S. H. Saker, D. O’Regan, R. P. Agarwal, Dynamic inequalities of Hardy and Copson type on time scales, Analysis 34 (4) (2014), 391-402.
Search in Google Scholar Back to article
M. Zakarya, M. Altanji, G. AlNemer, H. A. Abd El-Hamid, C. Cesarano, H. M. Rezk, Fractional Reverse Coposn’s Inequalities via Conformable Calculus on Time Scales, Symmetry 13 (4) (2021), 542.
Search in Google Scholar Back to article
C.-J. Zhao, W.-S. Cheung, On Hardy-Pachpatte-Copson’s Inequalities., The Scientific World Journal Volume 2014 (2014), 607347.
Search in Google Scholar Back to article

Copson-type Inequalities via the k-Hadamard Operator

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