Elhoucien Elqorachi, Mohamed Akkouchi

The Superstability of the Generalized d'Alembert Functional Equation

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 $G$.