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  Volume 10, Issue 4, Article 117
 
Arithmetic-Geometric-Harmonic Mean of Three Positive Operators

    Authors: Mustapha Ra´ssouli, Fatima Leazizi, Mohamed Chergui,  
    Keywords: Positive operator, Geometric operator mean, Arithmetic-geometric-harmonic operator mean.  
    Date Received: 18/12/2007  
    Date Accepted: 08/07/2009  
    Subject Codes:

15A48, 47A64.

 
    Editors: Fuad Kittaneh,  
 
    Abstract:

In this paper, we introduce the geometric mean of several positive operators defined from a simple and practical recursive algorithm. This approach allows us to construct the arithmetic-geometric-harmonic mean of three positive operators which has many of the properties of the standard one.

         
       
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