JIPAM

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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