journal6 ›› 2005, Vol. 26 ›› Issue (1): 60-63.

• Key disciplines • Previous Articles     Next Articles

An Improvement of the Inequality Similar to Hardy-Hilbert's Inequality


  1. (1.Department of Mathematics and Computer Science,Normal College,Jishou University,Jishou 416000,Hunan China;2.Department of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China)
  • Online:2005-01-15 Published:2012-09-22
  • About author:YAO Jin-bin(1963-),male,was born in Yongshun,Hunan Province,the senior lecturer;the major study field is real function and its application.

Abstract: In this paper,by means of the refined Cauchy’s inequality,a inequality similar to Hilbert’s inequality is improved.A new inequality is built:〖DD(〗∞〖〗n=1〖DD)〗〖DD(〗∞〖〗m=1〖DD)〗(ambn/(ln m+ln n+1)<π〖JB({〗〖DD(〗∞〖〗n=1〖DD)〗na2n〖DD(〗∞〖〗n=1〖DD)〗nb2n〖JB)}〗1/2(1-R)1/2.where R=〖JB((〗((α,γ)/‖α‖)-(β,γ)/‖β‖〖JB))〗2.

Key words: Hardy-Hilbert's inequality, Cauchy&rsquo, s inequality, weight coefficient

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