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  Volume 5, Issue 2, Article 49
 
The Stability of Some Linear Functional Equations
    Authors: Belaid Bouikhalene,  
    Keywords: Linear functional equations, Stability, Superstability.  
    Date Received: 14/01/04  
    Date Accepted: 25/04/04  
    Subject Codes:

39B72.

  
    Editors: Kazimierz Nikodem,  
 
    Abstract:

In this note, we deal with the Baker's superstability for the following linear functional equations

$displaystyle sum_{i=1}^{m} f(x+y+a_{i})= f(x)f(y),quadx,yin G,$    

$displaystyle sum_{i=1}^{m} [f(x+y+a_{i})+f(x-y-a_{i})]=2f(x)f(y),quadx,yin G,$    

where $ G$ is an abelian group, $ a_{1}, ldots, a_{m}$ ( $ m in mathbf{N}$) are arbitrary elements in $ G$ and $ f$ is a complex-valued function on $ G$.

         
       
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