ON HILBERT'S INTEGRAL INEQUALITY AND ITS APPLICATIONS

被引：0

作者：

Peng Xiuying ^{[1
]}

Gao Mingzhe ^{[2
]}

机构：

[1] Tech Sch Xiangxi Autonomous Prefecture, Jishou 416000, Hunan, Peoples R China

[2] Normal Coll Jishou Univ, Dept Math & Comp Sci, Jishou 416000, Hunan, Peoples R China

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2011年 / 14卷 / 02期

关键词：

Weight function; Hilbert's integral inequality; Schwarz's inequality; Widder's inequality; Hardy-Littlewood's inequality;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper it is shown that a new improvement on Hilbert's integral inequality can be established by introducing a weight function of the form (1/1+root x - 1/1+x) (with x >= 0). As applications, some refinements on Widder's inequality and Hardy-Littlewood's inequality are given.

引用

页码：271 / 279

页数：9

共 10 条

[1]

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[2]

Gao MZ, 1998, P AM MATH SOC, V126, P751

[3]

Gao MZ, 1997, J MATH ANAL APPL, V212, P316

[4]

Gradshteyn S., 2014, Table of Integrals, Series, and Products, V8th

[5]

Hardy Godfrey Harold, 1952, Inequalities, V2nd

[6]

HSU LC, 1990, J MATH RES EXP, V10, P500

[7]

HU K, 1979, J JIANGXI NORMAL COL, V1, P1

[8]

Mitrinovic J. E., 1991, Inequalities Involving Functions and Their Integrals and Derivatives

[9]

WIDDER O. V., 1924, J LOND MATH SOC, V4, P194

[10]

Zwillinger D., 1988, CRC STANDARD MATH TA

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