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    STUDIA MATHEMATICA - Issue no. 4 / 2014  
         
  Article:   BILATERAL INEQUALITIES FOR HARMONIC, GEOMETRIC AND HÖLDER MEANS.

Authors:  .
 
       
         
  Abstract:   For 0 < a < b, the harmonic, geometric and Hölder means satisfy H < G < Q. They are special cases (p = e-􀀀1, 0, 2) of power means Mp. We consider
the following problem: fi nd all α, β Î  R  for which the bilateral inequalities
αH(a,b) + (1-α􀀀 )Q(a,b) < G(a,b) < βH(a,b) + (1-β )Q(a,b)
hold " 0 < a < b. Then we replace in the bilateral inequalities the mean Q by
Mp, p > 0 and address the same problem.

Mathematics Subject Classiφι cation (2010): 26E60.
Keywords: Means, power means, bilateral inequalities.

 
         
     
         
         
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