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Hyers-Ulam Stability of the Generalized Quadratic Functional Equation in Amenable Semigroup  
 
  Authors: Belaid Bouikhalene, Elhoucien Elqorachi, Ahmed Redouani,  
  Keywords: Hyers-Ulam stability, Quadratic functional equation, Amenable semigroup, Morphism of semigroup.  
  Date Received: 06/03/07  
  Date Accepted: 26/04/07  
  Subject Codes:

39B82, 39B52.

  
  Editors: Themistocles M. Rassias,  
 
  Abstract:

In this paper we derive the Hyers-Ulam stability of the quadratic functional equation

$displaystyle f(xy)+f(xsigma(y))=2f(x)+2f(y),;;x,yin G,$
respectively the functional equation
$displaystyle f(xy)+g(xsigma(y))=f(x)+g(y),;;x,yin G,$
where $ G$ is an amenable semigroup, $ sigma$ is a morphism of $ G$ such that $ sigmacircsigma=I$, respectively where $ G$ is an amenable semigroup and $ sigma$ is an homomorphism of $ G$ such that $ sigmacircsigma=I$.;


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