IJPAM: Volume 46, No. 2 (2008)

ON INEQUALITIES OF THE HILBERT'S TYPE

Bing He$^1$, You Qian$^2$, Yongjin Li$^3$
$^1$Department of Mathematics
Guangdong Education College
Guangzhou, 510303, P.R. CHINA
e-mail: hzs314@163.com
$^{2,3}$Department of Mathematics
Institute of Logic and Cognition
Sun Yat-Sen University
Guangzhou, 510275, P.R. CHINA
e-mail: stslyj@mail.sysu.edu.cn


Abstract.By introducing the function $ \frac{\vert\ln{x}-\ln{y}\vert}{x+y+\max\{x,y\}}$, we establish a new inequalities similar to Hilbert's type inequality with the best constants factor.

Received: November 8, 2007

AMS Subject Classification: --???--

Key Words and Phrases: Hilbert's integral inequality, weight function, weight coefficient, Young's inequality

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 2