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  Volume 8, Issue 2, Article 46
Superquadracity of Functions and Rearrangements of Sets

    Authors: Shoshana Abramovich,  
    Keywords: Superquadratic functions, Convex functions, Jensen's inequality.  
    Date Received: 26/12/06  
    Date Accepted: 29/05/07  
    Subject Codes:


    Editors: Sever S. Dragomir,  

In this paper we establish upper bounds of

$displaystyle sum_{i=1}^{n}left( fleft( frac{x_{i}+x_{i+1}}{2}right) +fle... ...leftvert x_{i}-x_{i+1}rightvert }{2}right) right) , qquad x_{n+1}=x_{1}$

when the function $ f$ is superquadratic and the set $ left( mathbf{x}right) =left( x_{1},dots ,x_{n}right) $ is given except its arrangement.

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