An Exponential-logarithmic Maximum Hardy-Hilbert-type Integral Inequality
Abstract
This paper introduces a new variant of the Hardy-Hilbert integral inequality, referred to as an exponential-logarithmic maximum Hardy-Hilbert-type integral inequality. Using this result, we establish an additional related inequality. For completeness and accessibility, the paper is self-contained, and all proofs are provided in detail.
Downloads
References
Adiyasuren, V., Batbold, T., & Krnic, M. (2015). Hilbert-type inequalities involving differential operators, the best constants, and applications. Mathematical Inequalities & Applications, 18(1), 111-124. https://doi.org/10.7153/mia-18-07
Batbold, T., Krnic, M., Pecaric, J., & Vukovic, P. (2017). Further development of Hilbert-type inequalities / Selected topics in Hilbert-type inequalities (Monographs in Inequalities 13). Element.
Chen, Q., & Yang, B. C. (2015). A survey on the study of Hilbert-type inequalities. Journal of Inequalities and Applications, 2015(1), 1-29. https://doi.org/10.1186/s13660-015-0829-7
Chesneau, C. (2025). Two contributions to the absolute-value-Hardy-Hilbert-type integral inequalities. Asia Mathematika, 9(3), 12-19. https://doi.org/10.5281/zenodo.18607707
Chesneau, C. (2026). On a Hardy-Hilbert-type integral inequality involving an adjustable function. The Pecaric Journal of Mathematical Inequalities, 2(1), 22-28. https://doi.org/10.30538/pjmi2026.0017
Du, H., & Miao, Y. (2011). Several new Hardy-Hilbert's inequalities. Filomat, 25(3), 153-162. https://doi.org/10.2298/FIL1103153D
Hardy, G. H. (1925). Note on a theorem of Hilbert concerning series of positive terms. Proceedings of the London Mathematical Society, 23(2), 45-46.
Hardy, G. H., Littlewood, J. E., & Polya, G. (1934). Inequalities. Cambridge University Press.
Krnic, M., Pecaric, J., Peric, I., & Vukovic, P. (2012). Recent advances in Hilbert-type inequalities / A unified treatment of Hilbert-type inequalities (Monographs in Inequalities 3). Element.
Li, Y., Qian, Y., & He, B. (2007). On further analogs of Hilbert's inequality. International Journal of Mathematics and Mathematical Sciences, 2007, Article 39237, 1-6. https://doi.org/10.1155/2007/76329
Xu, J. S. (2007). Hardy-Hilbert's inequalities with two parameters. Advances in Mathematics (China), 36(1), 63-76.
Yang, B. C. (2009). The norm of operator and Hilbert-type inequalities. Science Press.
Yang, B. C. (2009). Hilbert-type integral inequalities. Bentham Science Publishers. https://doi.org/10.2174/97816080505501090101
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
