JIPAM

Inequalities Between the Sum of Squares and the Exponential of Sum of a Nonnegative Sequence  
 
  Authors: Feng Qi,  
  Keywords: Inequality, Sum of square, Exponential of sum, Nonnegative sequence, Critical point, Extremal point, Open problem.  
  Date Received: 11/04/07  
  Date Accepted: 08/09/07  
  Subject Codes:

26D15.

  
  Editors: Anthony Sofo,  
 
  Abstract:

Using a standard argument, the following inequality between the sum of squares and the exponential of sum of a nonnegative sequence is established:

$displaystyle frac{e^2}{4}{sum_{i=1}^nx_i^2}leexpBiggl(sum_{i=1}^nx_iBiggr), $
where $ nge2$, $ x_ige0$ for $ 1le ile n$, and the constant $ frac{e^2}{4}$ is the best possible. ;


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