A New Hilbert-Type Integral Inequality with Parameters
Received:May 09, 2009  Revised:September 18, 2009
Key Words: Hilbert-type integral inequality   hyperbolic cosecant function   Bernoulli number   weight function   best constant.  
Fund Project:Supported by the Project of Scientific Research Fund of Hunan Provincial Education Department (Grant No.09C789).
Author NameAffiliation
Xue Mei GAO Department of Mathematics & Computer Science, Normal College of Jishou University, Hunan 416000, P. R. China 
Ming Zhe GAO Department of Mathematics & Computer Science, Normal College of Jishou University, Hunan 416000, P. R. China 
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Abstract:
      In this paper it is shown that a new Hilbert-type integral inequality can be established by introducing two parameters $m~(m \in N)$ and $\lambda~(\lambda > 0)$. And the constant factor expressed by the Bernoulli number and $\pi$ is proved to be the best possible. And then some important and especial results are enumerated. As applications, some equivalent forms are given.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.03.011
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