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  Volume 9, Issue 2, Article 53
Refinements of Inequalities Between the Sum of Squares and the Exponential of Sum of a Nonnegative Sequence

    Authors: Yu Miao, Li-Min Liu, Feng Qi,  
    Keywords: Inequality, Exponential of sum, Nonnegative sequence, Normal random variable.  
    Date Received: 12/11/07  
    Date Accepted: 07/03/08  
    Subject Codes:

26D15; 60E15

    Editors: Anthony Sofo,  

Using probability theory methods, the following sharp inequality is established:

$displaystyle frac{e^k}{k^k} left(sum_{i=1}^nx_iright)^{k}leexpleft(sum_{i=1}^n x_iright),$    
where $ kinmathbb{N}$, $ ninmathbb{N}$ and $ x_ige 0$ for $ 1le ile n$. Upon taking $ k=2$ in the above inequality, the inequalities obtained in [F. Qi, Inequalities between the sum of squares and the exponential of sum of a nonnegative sequence, J. Inequal. Pure Appl. Math. 8(3) (2007), Art. 78 are refined.

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