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  Volume 3, Issue 3, Article 40
 
A Monotonicity Property of Power Means
    Authors: A.McD. Mercer,  
    Keywords: Arithmetic mean, Geometric mean, Monotonicity, Power means.  
    Date Received: 21/02/02  
    Date Accepted: 24/03/02  
    Subject Codes:

26D15

  
    Editors: Peter S. Bullen,  
 
    Abstract:

If $ A$ and $ G$ are the arithmetic and geometric means of the numbers $ %% x_{j}in (a,b)$, a family of inequalities is derived of which $ a+b-A>ab/G$ is a special case. These inequalities demonstrate a new monotonicity property for power means.

         
       
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