Let \(G\) be a topological group and \(\mu\) a compactly supported measure on \(G\). Moreover, let \(\sigma\) denote a continuous involution on \(G\). The authors consider the following functional equations: \[ \begin{aligned} &\int_G f(xty) d\mu(t)=g(x)f(y),\\ &\int_G f(xty) d\mu(t)+\int_G f(xt\sigma(y)) d\mu(t)=2f(x)g(y).\\ \end{aligned} \] The first equation generalizes Cauchy's and Pexider's equations, while the second one generalizes d'Alembert's and Wilson's equations. Some results about stability and superstability of the previous equations are proved.