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Some new generalisations of inequalities of Hardy and Levin–Cochran–Lee

  • Aleksandra C˘iz˘mes˘ija (a1) and Josip Pec˘arić (a2)
Abstract

In this paper finite versions of Hardy's discrete, Hardy's integral and the Levin–Cochran–Lee inequalities will be considered and some new generalisations of these inequalities will be derived. Moreover, it will be shown that the constant factors involved in the right-hand sides of the integral results obtained are the best possible.

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COPYRIGHT: © Australian Mathematical Society 2001
References
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[1]Bicheng, Y., Zhuohua, Z. and Debnath, L., ‘On new generalizations of Hardy's integral inequality’, J. Math. Anal. Appl. 217 (1998), 321–327.
[2]Bicheng, Y. and Debnath, L., ‘Generalizations of Hardy's integral inequalities’, Internat. J. Math. Math. Sci. 22 (1999), 535–542.
[3]Cochran, J.A. and Lee, C.-S., ‘Inequalities related to Hardy's and Heinig's’, Math. Proc. Cambridge Philos. Soc. 96 (1984), 1–7.
[4]C˘iz˘mes˘ija, A. and Pec˘arić, J., ‘Mixed means and Hardy's inequality’, Math. Inequal. Appl. 1 (1998), 491–506.
[5]C˘iz˘mes˘ija, A. and Pec˘carić, J., ‘Classical Hardy's and Carleman's inequalities and mixed means’, in Survey on Classical Inequalities, (Rassias, T. M., Editor) (Kluwer Academic Publishers, Dordrecht, Boston, London, 2000), pp. 27–65.
[6]Hardy, G., Littlewood, J.E. and Pólya, G., Inequalities, (second edition) (Cambridge University Press, Cambridge, 1967).
[7]Love, E.R., ‘Inequalities related to those of Hardy and of Cochran and Lee’, Math. Proc. Cambridge Philos. Soc. 99 (1986), 395–408.
[8]Mitrinović, D.S., Pečarić, J.E. and Fink, A.M., Inequalities involving functions and their integrals and derivatives (Kluwer Academic Publishers, Dordrecht, Boston, London, 1991).
[9]Mond, B. and Pec˘arić, J., ‘A mixed means inequality’, Austral. Math. Soc. Gazette 23 (1996), 67–70.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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