Abstract
By introducing the function
Research Article | Open Access
On Further Analogs of Hilbert's Inequality
Academic Editor: Laszlo Toth
Received08 May 2007
Accepted23 Aug 2007
Published04 Nov 2007
References
G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge, UK, 1934.
View at: Zentralblatt MATHG. H. Hardy, “Note on a theorem of Hilbert,” Mathematische Zeitschrift, vol. 6, no. 3-4, pp. 314–317, 1920.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, vol. 53 of Mathematics and Its Applications (East European Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.
View at: Zentralblatt MATH | MathSciNetY. C. Chow, “On inequalities of Hilbert and Widder,” Journal of the London Mathematical Society, vol. 14, no. 2, pp. 151–154, 1939.
View at: Publisher Site | Google Scholar | Zentralblatt MATHM. Gao, “On Hilbert's inequality and its applications,” Journal of Mathematical Analysis and Applications, vol. 212, no. 1, pp. 316–323, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Jichang, “On new extensions of Hilbert's integral inequality,” Journal of Mathematical Analysis and Applications, vol. 235, no. 2, pp. 608–614, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetB. G. Pachpatte, “Inequalities similar to the integral analogue of Hilbert's inequality,” Tamkang Journal of Mathematics, vol. 30, no. 2, pp. 139–146, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetB. Yang, “An extension of Hardy-Hilbert's inequality,” Chinese Annals of Mathematics, Series A, vol. 23, no. 2, pp. 247–254, 2002 (Chinese).
View at: Google Scholar | Zentralblatt MATH | MathSciNetY. Li, J. Wu, and B. He, “A new Hilbert-type integral inequality and the equivalent form,” International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 45378, 6 pages, 2006.
View at: Publisher Site | Google Scholar | MathSciNet
Copyright
Copyright © 2007 Yongjin Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.