摘要应用权系数方法给出新的带有最佳常数的Hilbert型不等式,同时给出其等价形式及逆向不等式.A new Hilbert＇s inequality with a best constant factor is obtined.An equivalent form and its reverse is given as well.
1Hardy G. H., Littlewood J. E., Polya G., Inequalities, London: Cambridge Univ. Press, 1952.
2Yang B. C., Debnath L., On a new generalization of Hardy-Hilbert's inequality and its application, J. Math.Anal. Appl., 1999, 233: 484-497.
3Mitrinovic D. S., Pecaric J. E., Fink A. M., Inequalities involving functions and their integrals and derivatives,Boston: Kluwer Academic Publishers, 1991.
4Yang B. C., Debnath L., Some inequalities involving π and an application to Hilbert's inequality, Applied Math. Letters, 1999, 129: 101-105.
5Yang B. C., On a strengthened version of the more accurate Hardy-Hilbert's inequality, Acta Mathematica Sinica, 1999, 42(6): 1103-1110 (in Chinese).
6Yang B. C., On a strengthened Hardy-Hilbert's inequality, J. Ineq. Pure and Appl. Math., 2000, 1(2): 22.
7Kuang J. C., Debnath L., On new generalizations of Hilbert's inequality and their applications, J. Math.Anal. Appl., 2000, 245: 248-265.
8Pachpatte B G., On some inequalities similar to Hilbert's inequality, J. Math. Anal. Appl., 1998, 226:166-179.
9Mulholland H. P., Some theorem on Dirichlet series with coefficients and related integrals, Proc. London Math. Soc., 1929, 29(2): 281-292.
3Hardy G H. Note on a theorem of Hilbert concerning series of positive terems[ J]. Proc London Math Soc,1925,23(2) :Recrds of Proc. XIV-XIVI.
4Xie Zitian,Zeng Zheng. A Hilbert-type integral inequality whose kernel is a homogeneous form of degree-3 [ J ]. J Math Appl,2008,339 ( 1 ) :324- 331.
5Yang Bicheng. On a new extension of a Hilbert-type integral inequality [ J ]. International Journal of Mathematical inequalities and Applications, 2007,1(1) :33-40.
6Xie Zitian, Yang Bicheng. A new Hilbert-type inequality with some parameters and its reverse [ J ]. Kyungpook Mathematical Journal,2008,48 ( 1 ) ;93-100.
