On certain generalizations of the Hardy inequality. (English) Zbl 1013.26017

In this paper, by introducing two parameters \(x\) and \(y\), some new generalizations of Carleman’s inequality and Hardy’s inequality are considered.


26D15 Inequalities for sums, series and integrals
26E60 Means
Full Text: DOI Euclid


[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
[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
[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
[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
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