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  Volume 6, Issue 2, Article 32
On Hyers-Ulam Stability of a Special Case of O'Connor's and Gajda's Functional Equations

    Authors: Belaid Bouikhalene, Elhoucien Elqorachi, Ahmed Redouani,  
    Keywords: Functional equations, Hyers-Ulam stability, Gelfand pairs.  
    Date Received: 08/11/04  
    Date Accepted: 01/03/05  
    Subject Codes:


    Editors: Kazimierz Nikodem,  

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

$displaystyle sum_{varphi in Phi }int_{K}f(xkvarphi (y)k^{-1})domega _{K}(k)=vertPhi vert a(x)overline{a(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,a:Glongrightarrow mathbb{C}$ are continuous complex-valued functions such that $ f$ satisfies the Kannappan type condition

$displaystyle int_{K}int_{K}f(zkxk^{-1}hyh^{-1})domega _{K}(k)domega _{K}(h)=int_{K}int_{K}f(zkyk^{-1}hxh^{-1})domega_{K}(k)domega _{K}(h),$ (*)

for all $ x,y,zin G.$

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