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  Volume 7, Issue 5, Article 162
 
A New Arrangement Inequality
    Authors: Mohammad Javaheri,  
    Keywords: Inequality, Arrangement.  
    Date Received: 29/04/06  
    Date Accepted: 17/11/06  
    Subject Codes:

26Dxx.

  
    Editors: Grahame Bennett,  
 
    Abstract:

In this paper, we discuss the validity of the inequality

$displaystyle sum_{i=1}^n x_i sum_{i=1}^n x^a_ix^b_{i+1} leq left(sum_{i=1}^n x^{(1+a+b)/2}_iright)^2 ,$

where $ 1,a,b$ are the sides of a triangle and the indices are understood modulo $ n$. We show that, although this inequality does not hold in general, it is true when $ nleq 4$. For general $ n$, we show that any given set of nonnegative real numbers can be arranged as $ x_1,x_2,ldots,x_n$ such that the inequality above is valid.

         
       
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