Lipschitzian solutions to linear iterative equations revisited
Karol Baron, Janusz Morawiec · Aequationes Mathematicae · 2017
We study the problems of the existence, uniqueness and continuous dependence of Lipschitzian solutions $$\varphi $$ of equations of the form $$\begin{aligned} \varphi (x)=\int _{\Omega }g(\omega )\varphi \big (f(x,\omega )\big )\mu (d\omega )+F(x), \end{aligned}$$ where $$\mu $$ is a measure on a $$\sigma $$ -algebra of subsets of $$\Omega $$ and $$\int _{\Omega }g(\omega )\mu (d\omega )\!=\!1$$ .