Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-07-06T08:59:54.870Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  17 April 2009

Aleksandra C˘iz˘mes˘ija  and
Josip Pec˘arić
Aleksandra C˘iz˘mes˘ija
Affiliation:
Department of Mathematics, University of Zagreb, Bijenic˘ka cesta 30, 10000 Zagreb, Croatia, e-mail: cizmesij@math.hr
Josip Pec˘arić
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, SA 5005, Australia, e-mail: jpecaric@maths.adelaide.edu.au
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 105 - 113
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Bicheng, Y., Zhuohua, Z. and Debnath, L., ‘On new generalizations of Hardy's integral inequality’, J. Math. Anal. Appl. 217 (1998), 321–327.CrossRefGoogle Scholar
[2]Bicheng, Y. and Debnath, L., ‘Generalizations of Hardy's integral inequalities’, Internat. J. Math. Math. Sci. 22 (1999), 535–542.CrossRefGoogle Scholar
[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.CrossRefGoogle Scholar
[4]C˘iz˘mes˘ija, A. and Pec˘arić, J., ‘Mixed means and Hardy's inequality’, Math. Inequal. Appl. 1 (1998), 491–506.Google Scholar
[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.Google Scholar
[6]Hardy, G., Littlewood, J.E. and Pólya, G., Inequalities, (second edition) (Cambridge University Press, Cambridge, 1967).Google Scholar
[7]Love, E.R., ‘Inequalities related to those of Hardy and of Cochran and Lee’, Math. Proc. Cambridge Philos. Soc. 99 (1986), 395–408.CrossRefGoogle Scholar
[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).CrossRefGoogle Scholar
[9]Mond, B. and Pec˘arić, J., ‘A mixed means inequality’, Austral. Math. Soc. Gazette 23 (1996), 67–70.Google Scholar