A Note on a Generalization of Two Integral Inequality Theorems
Abstract
In this article, we propose a general theorem that unifies two existing theorems on analogues of the Hilbert integral inequality. A key tool in our approach is the Young integral inequality. Detailed proofs are provided.
Downloads
References
Hardy, G. H., Littlewood, J. E., & Polya, G. (1934). Inequalities. Cambridge University Press.
Pachpatte, B. G. (2000). Inequalities similar to certain extensions of Hilbert's inequality. Journal of Mathematical Analysis and Applications, 243(2), 217-227. https://doi.org/10.1006/jmaa.1999.6646
Kim, Y. H., & Kim, B. I. (2002). An analogue of Hilbert's inequality and its extensions. Bulletin of the Korean Mathematical Society, 39(3), 377-388. https://doi.org/10.4134/BKMS.2002.39.3.377
Young, W. H. (1912). On classes of summable functions and their Fourier series. Proceedings of the Royal Deliverance Society of London, Series A, 87(594), 225-229. https://doi.org/10.1098/rspa.1912.0076
Zakarya, M., Saied, A. I., Al-Thaqfan, A. A. I., Ali, M., & Rezk, H. M. (2024). On some new dynamic Hilbert-type inequalities across time scales. Axioms, 13(7), 475. https://doi.org/10.3390/axioms13070475
Saied, A. I. (2024). A study on reversed dynamic inequalities of Hilbert-type on time scales nabla calculus. Journal of Inequalities and Applications, 2024(1), 75. https://doi.org/10.1186/s13660-024-03091-8
Rezk, H. M., Valdés, J. E. N., Ali, M., Saied, A. I., & Zakarya, M. (2024). Delta calculus on time scale formulas that are similar to Hilbert-type inequalities. Mathematics, 12(1), 104. https://doi.org/10.3390/math12010104
Zakarya, M., AlNemer, G., Saied, A. I., Butush, R., Bazighifan, O., & Rezk, H. M. (2022). Generalized inequalities of Hilbert-type on time scales nabla calculus. Symmetry, 14(8), 1512. https://doi.org/10.3390/sym14081512
AlNemer, G., Zakarya, M., Abd El-Hamid, H. A., Agarwal, P., & Rezk, H. M. (2020). Some dynamic Hilbert-type inequalities on time scales. Symmetry, 12(9), 1410. https://doi.org/10.3390/sym12091410
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
