賀樂平,劉 妥

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一個非齊次核的半離散型Hilbert型不等式的改進(jìn)

賀樂平*,劉 妥

(吉首大學(xué) 數(shù)學(xué)與統(tǒng)計學(xué)院, 湖南 吉首, 416000)

式(1)稱為Hardy-Hilbert積分不等式, 它在分析學(xué)中有重要的應(yīng)用.

文獻(xiàn)[1]給出了如下一個新的較精確的半離散Hilbert不等式:

1 引理及證明

為了方便起見, 先介紹一些符號:

證明見文獻(xiàn)[2].

證明過程見文獻(xiàn)[2].

2 主要結(jié)果

為方便起見, 再引入一些符號:

證明 由引理1和引理2, 有:

即(5)式得證.

,

注: 式(5)即為式(2)的改進(jìn)式.

[1] Yang Bicheng. A half-Discrete Hilbert-Type Inequality with a Non-Homogeneous kernel and two variables[J]. Mediterr J Math, 2012(12): 213—218.

[2] He Leping, Gao Mingzhe, Jia weijian. On a New Strengthened Hardy-Hilbert’sInequality[J]. Journal of Mathematical Research and Exposition, 2006, 26(2): 276—282.

[3] He Leping, Gao Mingzhe. A Hilbert Integral Inequality with Hurwitz Zeta Function[J]. Journal of Mathematical inequalities, 2013, 7(3): 377—387.

Improvement of half-discrete Hilbert-type inequality with non-homogeneous kernel

HE LePing, LIU Tuo

(College of Mathematics and Statistics, Jishou University, Jishou 416000, China)

Hilbert-type inequality are important in analysis and its applications. In this paper, a half-discrete Hilbert-type inequality is investigated. By using the way of weight functions and the techniuque of real analysis and a sharpening of H?lder’s inequality, some improvements of Hardy-Hilbert’s inequality are given, a few new inequalities are established.

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1672-6146(2014)01-0001-03

10.3969/j.issn.1672-6146.2014.01.001

通訊作者email: jdlepinghe@163.com.

2014-01-08

國家自然科學(xué)基金資助項目(11261020)

(責(zé)任編校:劉曉霞)