E. Elqorachi, M. Akkouchi

On Hyers-Ulam stability of Cauchy and Wilson Equations

We study the Hyers-Ulam stability problem for the Cauchy and Wilson integral equations
\int_{G}f(xty)d\mu(t)=f(x)g(y),\;\;x,y\in G,\\
\;\;x,y\in G,
where $G$ is a topological group, $f$, $g$ : $G\rightarrow \mathbb{C}$ are continuous functions, $\mu$ is a complex measure with compact support and $\sigma$ is a continuous involution of $G$. The result obtained in this paper are natural extensions of the previous works concerning the Hyers-Ulam stability of the Cauchy and Wilson functional equations done in the particular case of $\mu$=$\delta_{e}$: The Dirac measure concentrated at the identity element of $G$.

Topological group, Hyers--Ulam stability, Superstability, Cauchy equation, D'Alembert equation, Wilson equation.

MSC 2000: 39B72.