**Elhoucien Elqorachi, Mohamed Akkouchi**

## The Superstability of the
Generalized d'Alembert Functional Equation

**abstract:**

We generalize the well-known Baker's superstability result for the d'Alembert
functional equation with values in the field of complex numbers to the case of
the integral equation

$$\int_{G}f(xty)d\mu(t)+\int_{G}f(xt\sigma(y))d\mu(t)=2f(x)f(y)\;\;x,y\in G,$$

where $G$ is a locally compact group, $\mu$ is a generalized Gelfand measure and
$\sigma$ is a continuous involution of $G$.