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Multiple Hilbert and Hardy-Hilbert inequalities with non-conjugate parameters

Published online by Cambridge University Press:  17 April 2009

Ilko Brnetić ,
Mario Krnić  and
Josip Pečarić
Ilko Brnetić
Affiliation:
Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, Zagreb, Croatia, e-mail: ilko.brnetic@fer.hr
Mario Krnić
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia, e-mail: krnic@math.hr
Josip Pečarić
Affiliation:
Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia, e-mail: pecaric@hazu.hr
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The main objective of this paper is a study of some new generalisations of Hilbert and Hardy-Hilbert type inequalities involving non-conjugate parameters. We prove general forms of multiple Hilbert-type inequalities, and we also introduce multiple inequalities of Hardy-Hilbert type with non-conjugate parameters.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 447 - 457
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Bicheng, Y. and Rassias, T.M., ‘On the way of weight coefficients and research for the Hilbert-type inequalities’, Math. Inequal. Appl. 6 (2003), 625–658.Google Scholar
[2]Bicheng, Y., Brnetić, I., Krnić, M. and Pečarić, J., ‘Generalization of Hilbert and Hardy-Hilbert integral inequality’, Math. Inequal. Appl. (to appear).Google Scholar
[3]Bonsall, F.F., ‘Inequalities with non-conjugate parameters’, Quart. J. Math. Oxford 2 (1951), 135–150.CrossRefGoogle Scholar
[4]Brnetić, I. and Pečarić, J., ‘Generalization of Hilbert's integral inequality’, Math. Inequal. Appl. 7 (2004), 199–205.Google Scholar
[5]Brnetić, I. and Pečarić, J., ‘Generalization of inequalities of Hardy-Hilbert's type’, Math. Inequal. Appl. 7 (2004), 217–225.Google Scholar
[6]Čižmešija, A., Krnić, M. and Pečarić, J., ‘General Hilbert's inequality with non-conjugate parameters’, (submitted).Google Scholar
[7]Hardy, G.H., Littlewood, J.E. and Pólya, G., Inequalities (Cambridge Univ. Press, Cambridge, 1952).Google Scholar
[8]Krnić, M. and Pečarić, J., ‘General Hilbert's and Hardy's inequalities’, Math. Inequal. Appl. (to appear).Google Scholar