JIPAM

On the Stability of A Class of Functional Equations  
 
  Authors: Belaid Bouikhalene,  
  Keywords: Functional equation, Stability, Superstability, Central function, Gelfand pairs.  
  Date Received: 20/07/03  
  Date Accepted: 24/10/03  
  Subject Codes:

39B72

  
  Editors: Kazimierz Nikodem,  
 
  Abstract:

In this paper, we study the Baker's superstability for the following functional equation

$displaystyle sum_{varphi in Phi }int_{K}f(xkvarphi (y)k^{-1})domega _{K}(k)$

$ Eleft( Kright) $
$displaystyle =vertPhi vert f(x)f(y), x,yin G$

where $ G$ is a locally compact group, $ K$ is a compact subgroup of $ G$, $ omega _{K}$ is the normalized Haar measure of $ K$, $ Phi $ is a finite group of $ K$-invariant morphisms of $ G$ and $ f$ is a continuous complex-valued function on $ G$ satisfying the Kannappan type condition, for all $ x,y,zin G$

$displaystyle int_{K}int_{K}f(zkxk^{-1}hyh^{-1})domega _{K}(k)domega _{K}(h)qquadqquadqquadqquad$

(*)
 
$displaystyle =int_{K}int_{K}f(zkyk^{-1}hxh^{-1})domega _{K}(k)domega _{K(h).$
We treat examples and give some applications. ;


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