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An Extension of the Erdös-Debrunner Inequality to General Power Means  
 
  Authors: Vania Mascioni,  
  Keywords: Erdös-Debrunner inequality, harmonic mean, geometric mean, power means  
  Date Received: 07/04/07  
  Date Accepted: 08/07/08  
  Subject Codes:

Pri: 26D15, Sec: 26D20, 51M16

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

Given the harmonic mean $ mu$ of the numbers $ x_i$ ($ i=1,2,3$) and a $ tin (0, min{x_1,x_2,x_3}/mu})$, we determine the best power mean exponents $ p$ and $ q$ such that $ M_p(x_i- tmu) leq (1- t)mu leq M_q(x_i- tmu)$, where $ p$ and $ q$ only depend on $ t$. Also, for $ t>0$ we similarly handle the estimates $ M_p(x_i+ tmu) leq (1+ t)mu leq M_q(x_i+ tmu)$.;


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