JIPAM

The Best Constant For An Algebraic Inequality  
 
  Authors: Y.N. Aliyev,  
  Keywords: Best constant, Geometric inequality, Euler's inequality.  
  Date Received: 27/03/06  
  Date Accepted: 02/06/07  
  Subject Codes:

52A40, 26D05.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

We determine the best constant $ lambda $ for the inequality $ frac{1}{x}+ frac{1}{y}+frac{1}{z}+frac{1}{t}geq frac{lambda }{1+16(lambda -16)xyzt};$ where $ x,y,z,t>0;$ $ x+y+z+t=1$. We also consider an analogous inequality with three variables. As a corollary we establish a refinement of Euler's inequality. ;


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