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  Volume 10, Issue 4, Article 95
 
Inequalities for $J-$Contractions Involving the $ \alpha-$Power Mean

    Authors: G. Soares,  
    Keywords: $J-$selfadjoint matrix, Furuta inequality, $J-$chaotic order, $lpha-$power mean.  
    Date Received: 22/06/2009  
    Date Accepted: 14/10/2009  
    Subject Codes:

47B50, 47A63, 15A45.

 
    Editors: Sever S. Dragomir,  
 
    Abstract:

A selfadjoint involutive matrix $J$ endows $ mathbb{C}^n$ with an indefinite inner product $[ cdot,  cdot]$ given by $[x,y]:= langle J x, y rangle$, $x,y in mathbb{C}^n.$ We present some inequalities of indefinite type involving the $ alpha-$power mean and the chaotic order. These results are in the vein of those obtained by E. Kamei [6, 7].

         
       
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