| 一类新的带参数的Hilbert 型积分不等式 |
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| 引用本文： | 高雪梅,高明哲. 一类新的带参数的Hilbert 型积分不等式[J]. 数学研究及应用, 2011, 31(3): 467-473. DOI: 10.3770/j.issn:1000-341X.2011.03.011 |
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| 作者姓名： | 高雪梅 高明哲 |
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| 作者单位： | 吉首大学师范学院数学与计算机科学系, 湖南 吉首 416000;吉首大学师范学院数学与计算机科学系, 湖南 吉首 416000 |
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| 基金项目： | 湖南省教育厅资助科研项目(Grant No.09C789). |
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| 摘 要： | In this paper it is shown that a new Hilbert-type integral inequality can be established by introducing two parameters m（m ∈ N） and λ（λ 0）.And the constant factor expressed by the Bernoulli number and π is proved to be the best possible.And then some important and especial results are enumerated.As applications,some equivalent forms are given.
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| 关 键 词： | Hilbert-type integral inequality hyperbolic cosecant function Bernoulli number weight function best constant. |
| 收稿时间： | 2009-05-09 |
| 修稿时间： | 2009-09-18 |
A New Hilbert-Type Integral Inequality with Parameters |
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| Xue Mei GAO and Ming Zhe GAO. A New Hilbert-Type Integral Inequality with Parameters[J]. Journal of Mathematical Research with Applications, 2011, 31(3): 467-473. DOI: 10.3770/j.issn:1000-341X.2011.03.011 |
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| Authors: | Xue Mei GAO and Ming Zhe GAO |
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| Affiliation: | 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. |
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| Keywords: | Hilbert-type integral inequality hyperbolic cosecant function Bernoulli number weight function best constant. |
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