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On inequalities of Hilbert's type

Published online by Cambridge University Press:  17 April 2009

Yongjin Li  and
Bing He
Yongjin Li
Affiliation:
Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, People's Republic of China e-mail: stslyj@mail.sysu.edu.cn
Bing He
Affiliation:
Department of Mathematics, Guangdong Education College, Guangzhou 510303, People's Republic China e-mail: hzs314@163.com
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By introducing the function 1/(min{x, y}), we establish several new inequalities similar to Hilbert's type inequality. Moreover, some further unification of Hardy-Hilbert's and Hardy-Hilbert's type integral inequality and its equivalent form with the best constant factor are proved, which contain the classic Hilbert's inequality as special case.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 1 , August 2007 , pp. 1 - 13
Copyright
Copyright © Australian Mathematical Society 2007

References

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