| 一个Hilbert型不等式及其等价形式的加强推广 |
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| 引用本文： | 黄启亮.一个Hilbert型不等式及其等价形式的加强推广[J].数学杂志,2010,30(3). |
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| 作者姓名： | 黄启亮 |
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| 作者单位： | 广东教育学院数学系,广东,广州,510303 |
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| 基金项目： | 广东高校自然科学重点研究项目，广东教育学院中青年骨干教师培养基金 |
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| 摘 要： | 本文研究了Hilbert型级数不等式.利用改进的Euler-Maclaurin求和公式及权系数的方法,并引进两对共轭指数,获得一个具有最佳常数系数的Hilbert型不等式,该不等式是联系若干Hilbert型不等式的加强推广式.作为应用,给出该不等式的等价形式及若干有意义的特殊结果.
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| 关 键 词： | Hilbert型不等式 等价形式 权系数 共轭指数 Euler-Maclaurin求和公式 |
ON A STRENGTHENED AND GENERALIZED HILBERT-TYPE INEQUALITY AND ITS EQUIVALENT FORM |
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| HUANG Qi-liang.ON A STRENGTHENED AND GENERALIZED HILBERT-TYPE INEQUALITY AND ITS EQUIVALENT FORM[J].Journal of Mathematics,2010,30(3). |
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| Authors: | HUANG Qi-liang |
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| Institution: | HUANG Qi-liang (Dept.of Math.,Guangdong Institute of Education,Guangzhou 510303,China) |
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| Abstract: | In this article,we study the Hilbert-type inequality.By using the improved Euler-Maclaurin's summation formula and estimating the weight coefficient and introducing two pairs of indexes of conjugate,we get a Hilbert-type inequality with a best constant coefficient which is a strengthened and generalized form of some early Hilbert-type inequalities.As applications,we also consider the equivalent form of this inequality and deal with some particulars. |
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| Keywords: | Hilbert-type inequality equivalent form weight coefficient index of conjugate Euler-Maclaurin's summation formula |
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