On a New Integral Inequality Derived from the Hardy-Hilbert Integral Inequality
Abstract
This article is devoted to a new integral inequality expressed in terms of elementary integrals. The proof is notable for its use of the classical Hardy-Hilbert integral inequality, which provides an elegant and concise argument. As an illustration of its utility, we also present an application to the gamma function.
References
Hardy, G. H., Littlewood, J. E., & Pólya, G. (1934). Inequalities. Cambridge: Cambridge University Press.
Beckenbach, E. F., & Bellman, R. (1961). Inequalities. Berlin: Springer. https://doi.org/10.1007/978-3-642-64971-4
Walter, W. (1970). Differential and integral inequalities. Berlin: Springer. https://doi.org/10.1007/978-3-642-86405-6
Bainov, D., & Simeonov, P. (1992). Integral inequalities and applications. Mathematics and Its Applications (Vol. 57). Dordrecht: Kluwer Academic.
Cvetkovski, Z. (2012). Inequalities: Theorems, techniques and selected problems. Berlin: Springer. https://doi.org/10.1007/978-3-642-23792-8
Carlson, F. (1934). Une inégalité. Arkiv för Matematik, Astronomi och Fysik, 25B, 1–5.
Gradshteyn, I. S., & Ryzhik, I. M. (2007). Table of integrals, series, and products (7th ed.). San Diego, CA: Academic Press.
Yang, B. C. (1998). On Hilbert's integral inequality. Journal of Mathematical Analysis and Applications, 220, 778–785. https://doi.org/10.1006/jmaa.1997.5877
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