Iterative functional equations in the class of Lipschitz functions

Summary.

Using a fixed point method we investigate the existence of Lipschitzian solutions of the iterative functional equation¶¶$\sum\limits_{i=1}^{\infty} \alpha_{i} f^{i}(x) = F(x)\ {\rm for}\ x \in \mathbb{B},$¶¶ where $\mathbb{B}$ is a compact convex subset of $\mathbb{R}^N$, and $F : \mathbb{B} \to \mathbb{B}$ is a given Lipschitz function.