A Reverse Hilbert's Type Inequality

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Abstract:

In this paper, by using the Euler-Maclaurin expansion, we establish an inequality of a weight coefficient. Using this inequality, we derive a reverse Hilbert's type inequality. As applications, an equivalent form is obtained.

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106-109

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December 2014

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© 2015 Trans Tech Publications Ltd. All Rights Reserved

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[1] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, (1934).

Google Scholar

[2] M. Krnic and J. Pecaric, General Hilbert's and Hardy's inequalities, Math. Inequal. Appl., 8. 1(2005): 29-51.

Google Scholar

[3] Jichang Kuang, Applied Inequalities, Sandong Science and Technology Press, Jinan, (2004).

Google Scholar

[4] Jichang Kuang and L. Debnath, On new generalizations of Hilbert's inequality and their applications, J. Math. Anal. Appl., 245(2000): 248-265.

Google Scholar

[5] Gaowen Xi, On generalizations and reinforcements of a Hilbert's type inequality, Rocky Mountain Journal of Mathematics, 42. 1(2012): 329-337.

DOI: 10.1216/rmj-2012-42-1-329

Google Scholar

[6] B. Yang, A new Hilbert-type inequality, Bull. Belg. Math. Soc., 13(2006): 479-487.

Google Scholar

[7] Bicheng Yang, A Reverse of the Hardy-Hilbert's Type Inequality, } Mathematics In Practice and Theory, 36: 11(2006): 207-212.

Google Scholar

[8] Bicheng Yang, On An Extension of Hardy-Hilbert's Inequality with A Parameter, } Mathematics In Practice and Theory, 36: 4(2006): 226-231.

Google Scholar

[9] B. Yang, On best extensions of Hardy-Hilbert's inequality with two parameters, J. Inequal. Pure Appl. Math., 6. 3(2005): Article 81.

Google Scholar

[10] B. Yang and J. Zhu, Inequality on the Hurwitz Zeta-function restricted to the axis of positive reals, Acta Scientiarum Naturalium Universitatis Sunyatseni, 36. 2(1997): 30-35.

Google Scholar