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  Volume 5, Issue 3, Article 73
 
A New Proof of the Monotonicity Property of Power Means
    Authors: Alfred Witkowski,  
    Keywords: Convexity, Monotonicity, Power Means  
    Date Received: 14/02/04  
    Date Accepted: 02/07/04  
    Subject Codes:

26D15

  
    Editors: Peter S. Bullen,  
 
    Abstract:

If $ M_r$ is the weighted power mean of the numbers $ x_jin[a,b]$ then $ Q_r(a,b,x)=left(a^r + b^r -M_r^rright)^{1/r}$ is increasing in $ r$. A new proof of this fact is given.

         
       
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