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Inequalities for power-exponential functions  
 
  Authors: Feng Qi, Lokenath Debnath,  
  Keywords: Inequality, power-exponential function, revised Cauchy's mean-value theorem in integral form.  
  Date Received: 05/11/99  
  Date Accepted: 10/04/00  
  Subject Codes:

26D07,26D20

  
  Editors: Peter S. Bullen,  
 
  Abstract:

The following inequalities for power-exponential functions are proved

$displaystyle frac{y^{x^y}}{x^{y^x}}>frac{y}x>frac {y^x}{x^y},quadleft(frac{y} xight)^{xy}>frac{y^y}{x^x},$

where $ 0xy1$ or $ 1xy$. ;


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