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Volume 1, Issue 2, 2000

Article 22

http://jipam.vu.edu.au/v1n2/012_00.html

ON A STRENGTHENED HARDY-HILBERT INEQUALITY

BICHENG YANG
E-Mail: bcyang@163.net

DEPARTMENT OF MATHEMATICS 
GUANGDONG EDUCATION COLLEGE 
GUANGZHOU, GUANGDONG 510303
PEOPLE'S REPUBLIC OF CHINA

Received 8 May, 2000; accepted 10 June 2000.
Communicated by: L. Debnath


In this paper, a new inequality for the weight coefficient $W(n,r)$ of the form
\begin{eqnarray*}
W\left( n,r\right) &=&\sum_{m=0}^{\infty }\frac{1}{m+n+1}\left...
...frac{1}{13\left(
n+1\right) \left( 2n+1\right) ^{1-\frac{1}{r}}}
\end{eqnarray*}
for $r>1,\;n\in N_{0}=N\cup \left\{ 0\right\}$ is proved. This is followed by a strengthened version of the more accurate Hardy-Hilbert inequality.
Key words:
Hardy-Hilbert inequality, weight coefficient, Hölder's inequality.

2000 Mathematics Subject Classification:
26D15.


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Other papers in this issue

Ostrowski type inequalities from a linear functional point of view
I. Gavrea and B. Gavrea

A Grüss type inequality for sequences of vectors in inner product spaces and applications
S.S. Dragomir

On an Bojanic-Stanojevic type inequality
Z. Tomovski

Regularity results for vector fields of bounded distortion and applications
A. Fiorenza and F. Giannetti

Inequalities for power-exponential functions
F. Qi and L. Debnath

On the generalized strongly nonlinear implicit quasivariational inequalities for set-valued mappings
Y.J. Cho, Z. He, Y. F. Cao and N. J. Huan

A new look at Newton's inequalities
C. P. Niculescu

An application of almost increasing and d-quasi monotone sequences
H. Bor

Several integral inequalities
F. Qi

On integral inequalities of Gronwall-Bellman-Bihari type in several variables
J. A. Oguntuase

Some inequalities for the expectation and variance of a random variable whose PDF is n-time differentiable
N.S. Barnett, P. Cerone, S.S. Dragomir and J. Roumeliotis

On a Strengthened Hardy-Hilbert Inequality
B. Yang

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© 2000 School of Communications and Informatics, Victoria University of Technology. All rights reserved.
JIPAM is published by the School of Communications and Informatics which is part of the Faculty of Engineering and Science, located in Melbourne, Australia. All correspondence should be directed to the editorial office.

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