JIPAM

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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