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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 542-543Some Extensions of Hilbert-Type Inequalities

Some Extensions of Hilbert-Type Inequalities

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Abstract:

In this paper, an extension of Hilbert-type inequalities with a best constant factor is given by introducing two parameter .

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Periodical:

Advanced Materials Research (Volumes 542-543)

Pages:

1403-1406

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.542-543.1403

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Online since:

June 2012

Authors:

Bao Ju Sun

Keywords:

Hilbert’s Type Inequality, Hölder Inequality, Weight Function

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© 2012 Trans Tech Publications Ltd. All Rights Reserved

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[1] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Gambridge University Press, Gambridge, UK, 2 nd edition, 1952.

[2] M. Gao and B. Yang, "On the extended Hilbert's inequality", Proceeding of the American Mathematical Society, vol.126, no.3, pp.751-759, 1998.

[3] K. Jichang and L. Debnath, "On new generalizations of Hilbert's inequality and their applications", Journal of Mathematical Analysis and Applications, vol. 245, no.1, pp.248-265, 2000.

DOI: 10.1006/jmaa.2000.6766

[4] B. G. Pachpatte, "On some inequalities similar to Hilbert's inequality", Journal of Mathematical Analysis and Applications, vol. 226, no.1, pp.166-179, 1998.

DOI: 10.1006/jmaa.1998.6043

[5] B. Yang, "On an extension of Hardy-Hilbert's integral inequality", Chinese Annals of Mathematics, Series A, vol. 23, no. 2, pp.247-254, 2002 (Chinese).

[6] B. Yang, "On a generalization of the Hilbert's type integral inequality and its applications", Chinese Journal of Engineering Mathematics, vol. 21, no.5, pp.821-824, 2004(Chinese).

[7] Y. Li, Z. Wang and B. He, "Hilbert's type line operator and some extensions of Hilbert's inequality", Journal of Inequalities and Applications, vol. 2007, Article ID 82138, 10 pages, 2007.