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  Volume 3, Issue 3, Article 43
 
Inequalities on Linear Functions and Circular Powers
    Authors: Pantelimon Stanica,  
    Keywords: Binary Sequences, Fibonacci Numbers, Linear Forms, Inequalities.  
    Date Received: 25/02/02  
    Date Accepted: 10/04/02  
    Subject Codes:

11B37,11B39,26D15.

  
    Editors: Constantin P. Niculescu,  
 
    Abstract:

We prove some inequalities such as

$displaystyle F(x_1^{x_{sigma(1)}},ldots,x_n^{x_{%% sigma(n)}})leq F(x_1^{x_1},ldots,x_n^{x_n}),$
where $ F$ is a linear function or a linear function in logarithms and $ sigma$ is a permutation, which is a product of disjoint translation cycles. Stronger inequalities are proved for second-order recurrence sequences, generalizing those of Diaz.

         
       
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