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  Volume 8, Issue 3, Article 78
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:


    Editors: Anthony Sofo,  

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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