  We study the problems of the existence, uniqueness and continuous dependence
of Lipschitzian solutions $\varphi$ of equations of the form $$
\varphi(x)=\int_{\Omega}g(\omega)\varphi\big(f(x,\omega)\big)\mu(d\omega)+F(x),
$$ where $\mu$ is a measure on a $\sigma$-algebra of subsets of a set $\Omega$.
