journal6 ›› 2008, Vol. 29 ›› Issue (1): 26-28.

• Mathematics • Previous Articles     Next Articles

Refinement of Hardy-Hilbert Type Inequalities with Parameters


  1. (1.Zhangjiajie College of Jishou University,Zhangjiajie  427000,Hunan China;2.College of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China)
  • Online:2008-01-25 Published:2012-05-26

Abstract: An improvement of Hardy-Hilbert’s inequality can be obtained by means of a sharpening of Hlder’s inequality,a newinequality of the form  ∞n=0∞m=0(ambn/((2m+1)λ+(2n+1)λ)<π/(2λsin(π/p)){∞m=0(2m+1)p-1-λapm}1/p{∞n=0(2n+1)q-1-λbqn}1/q(1-R)kis built.

Key words:  Hardy-Hilbert inequality;Hlder inequality;&beta, function

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