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  Volume 5, Issue 4, Article 100
 
On Hyers-Ulam Stability of Generalized Wilson's Equation
    Authors: Belaid Bouikhalene,  
    Keywords: Functional equations, Hyers-Ulam stability, Wilson equation, Gelfand pairs.  
    Date Received: 20/05/04  
    Date Accepted: 15/09/04  
    Subject Codes:

39B72.

  
    Editors: Laszlo Losonczi,  
 
    Abstract:

In this paper, we study the Hyers-Ulam stability problem for the following functional equation

$displaystyle sum_{varphi in Phi }int_{K}f(xkvarphi (y)k^{-1})domega _{K}(k)=vertPhi vert f(x)g(y), x,yin G,$ ($ E(K)$)

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,g:Glongrightarrow mathbb{C}$ are continuous complex-valued functions such that $ f$ satisfies the Kannappan type condition, for all $ x,y,zin G$
begin{multline} int_{K}int_{K}f(zkxk^{-1}hyh^{-1})domega _{K}(k)domega _{K}... ...nt_{K}int_{K}f(zkyk^{-1}hxh^{-1})domega _{K}(k)domega _{K}(h). end{multline}

Our results generalize and extend the Hyers-Ulam stability obtained for the Wilson's functional equation.

         
       
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