On进一步强化了Hardy-Hilbert不等式

IF 1 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2004-01-01 DOI:10.1155/S0161171204205270

Lü Zhongxue

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引用次数: 0

摘要

我们得到一个不平等for the weight coefficientω(q, n)(1美元= id“E2”xmlns: mml = >“http://www.w3.org/1998/Math/MathML q > 1, q - q + 1 = 1, n∈ℕ)在theformω(q, m = 1∞(n) =:∑1 / (m + n) (n / m) 1 p - qπ(π/辛)−1 / (2 n / p + (1 / a) n−1 / q)在0 - a美国147 - 45,n≥3;0 1−C (a) / C(2−1),美国n = 1, 2和C是一个Eulerconstant。我们向大家展示由杨和黛纳特出售的文件的结果。

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On further strengthened Hardy-Hilbert's inequality

We obtain an inequality for the weight coefficient ω ( q , n ) ( 1$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"> q > 1 , 1 / q + 1 / q = 1 , n ∈ ℕ ) in the form ω ( q , n ) = : ∑ m = 1 ∞ ( 1 / ( m + n ) ) ( n / m ) 1 / q π / sin ( π / p ) − 1 / ( 2 n 1 / p + ( 2 / a ) n − 1 / q ) where 0 a 147 / 45 , as n ≥ 3 ; 0 a ( 1 − C ) / ( 2 C − 1 ) , as n = 1 , 2 , and C is an Euler constant. We show a generalization and improvement of Hilbert's inequalities. The results of the paper by Yang and Debnath are improved.

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来源期刊

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Mathematics-Mathematics (miscellaneous)

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

17 weeks

期刊介绍： The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.