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Hyers-Ulam stability of the Generalized Trigonometric Formulas  
 
  Authors: Ahmed Redouani, Elhoucien Elqorachi, Belaid Bouikhalene,  
  Keywords: Locally compact group, Functional equation, Hyers-Ulam stability, Superstability.  
  Date Received: 14/09/05  
  Date Accepted: 14/11/05  
  Subject Codes:

39B42, 39B32.

  
  Editors: Themistocles M. Rassias,  
 
  Abstract:

In this paper, we will investigate the Hyers-Ulam stability of the following functional equations

begin{displaymath} int_{G}int_{K}f(xtkcdot y) dkdmu(t)=f(x)g(y)+g(x)f(y), ;; x, y in G end{displaymath}

and
begin{displaymath} int_{G}int_{K}f(xtkcdot y) dkdmu(t)=f(x)f(y)-g(x)g(y), ;; x, y in G, end{displaymath}

where $K$ is a compact subgroup of morphisms of $G$, $dk$ is a normalized Haar measure of $K$, $mu$ is a complex $K$-invariant measure with compact support, the functions $f,g$ are continuous on $G$ and $f$ is assumed to satisfies the Kannappan type condition $K(mu)$
begin{displaymath} int_{G}int_{G}f(ztxsy)dmu(t)dmu(s)=int_{G}int_{G}f(ztysx)dmu(t)dmu(s), ;x,y,zin G. end{displaymath}

The paper of Székelyhidi [30] is the essential motivation for the present work and the methods used here are closely related to and inspired by those in [30].
The concept of the generalized Hyers-Ulam stability of mappings was introduced in the subject of functional equations by Th. M. Rassias in [20].;


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