A further generalization of Hardy-Hilbert's integral inequality with parameter and applications

• Autorzy: He L. , Dragomir S. S. , Yang Q.
• Języki publikacji: EN

Abstrakty

EN

In this paper, by introducing some parameters and by employing a sharpening of Hölder's inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder's theorem is given.

Słowa kluczowe

EN

Hardy-Hilbert's integral inequality; Holder's inequality; weight coefficient; beta function; Widder's theorem.

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2006
• Tom: Vol. 12, nr 1
• Strony: 59--70
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

He L.

autor

Dragomir S. S.

autor

Yang Q.

• Department of Mathematics and Computer Science. Jishou University, Jishou, Hunan 416000 People's Republic of China,

Bibliografia

• [1] Gao, Mingzhe, On the Hilbert inequality, Z. Anal. Anwendungen 18(4) (1999),1117-1122.
• [2] Gao, Mingzhe, Li, Tan, Debnath, L., Some improvements on Hilbert's integral inequality, J. Math. Anal. Appl. 229 (1999), 682-689.
• [3] Gao, Mingzhe, Wei, Shangrong, He, Leping, On the Hilbert inequality with weights, Z.Anal. Anwendungen 21(1) (2002), 257-263.
• [4] Hardy, G. H., Littlewood, J. E., Polya, G., Inequalities, Cambridge Univ. Press, Cambridge, 1952.
• [5] He, Leping, Gao, Mingzhe, Jia, Weijian , On the improvement of the Hardy-Hilbert’s integral inequality with parameters, JIPAM J. Inequal. Pure Appl. Math. 4(5) (2003), Art.94, [ONLINE: http://jipam.vu.edu.au/v4n5/108_03.html].
• [6] He, Leping, Gao, Mingzhe, Wei, Shangrong, A note on Hilbert's inequality, Math. Inequal. Appl. 6(2) (2003), 283-288.
• [7] Widder, D. V., An inequality related to one of Hilbert's, J. London Math. Soc. 4 (1924),194-198.
• [8] Yang, Bicheng, On Hardy-Hilbert's integral inequality, J. Math. Anal. Appl. 261 (2001),295-306.