Kim, Young-Ho On certain generalizations of the Hardy inequality. (English) Zbl 1013.26017 Proc. Japan Acad., Ser. A 78, No. 6, 101-104 (2002). In this paper, by introducing two parameters \(x\) and \(y\), some new generalizations of Carleman’s inequality and Hardy’s inequality are considered. Reviewer: Bicheng Yang (Guangzhou, Guangdong) MSC: 26D15 Inequalities for sums, series and integrals 26E60 Means Keywords:Carleman’s inequality; Hardy’s inequality; monotonicity PDFBibTeX XMLCite \textit{Y.-H. Kim}, Proc. Japan Acad., Ser. A 78, No. 6, 101--104 (2002; Zbl 1013.26017) Full Text: DOI Euclid References: [1] Beckenbach, E. F., and Bellman, R.: Inequalities. Springer-Verlag, Berlin-New York (1961). [2] Yang, B., and Debnath, L.: Some inequalities involving the constant \(e\), and an application to Carleman’s inequality. J. Math. Anal. Appl., 223 , 347-353 (1998). · Zbl 0910.26011 · doi:10.1006/jmaa.1997.5617 [3] Davis, G. S., and Peterson, G. M.: On an inequality of Hardy’s (II). Quart. J. Math. (Oxford), 15 , 35-40 (1964). · Zbl 0138.03406 · doi:10.1093/qmath/15.1.35 [4] Hardy, G. H., Littlewood, J. E., and Polya, G.: Inequalities. Cambridge Univ. Press, London (1952). [5] Kim, Y.-H.: Refinements and extensions of an inequality. J. Math. Anal. Appl., 245 , 628-632 (2000). · Zbl 0951.26009 · doi:10.1006/jmaa.2000.6734 [6] Németh, J.: Generalizations of the Hardy-Littlewood inequality. Acta Sci. Math. (Szeged), 32 , 295-299 (1971). · Zbl 0226.26020 [7] Yang, X.: Approximations for constant \(e\) and their applications. J. Math. Anal. Appl., 252 , 994-998 (2000). · Zbl 0988.26017 · doi:10.1006/jmaa.2001.7592 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.