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

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

Previous issues

Volume 1, Issue 1, 2000