JIPAM

A New Upper Bound of the Logarithmic Mean  
 
  Authors: Gao Jia, Jinde Cao,  
  Keywords: Logarithmic mean; Power mean; Heron mean; Best constant.  
  Date Received: 26/06/03  
  Date Accepted: 05/11/03  
  Subject Codes:

26D15,26D10.

  
  Editors: Jozsef Sandor,  
 
  Abstract:

Let $ a$ and $ b$ be positive numbers with $ a ne b$. The inequalities aboutthe logarithmic-mean

$displaystyle L(a,b)H_{p}(a,b)M_q(a,b)$   
are obtained, where $ pge frac{1}{2}$ and $ qge frac{2}{3}p$. We would point out that $ p=frac{1}{2}$ and $ q=frac{1}{3}$ are the best constants such that above inequalities hold.;


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