Iterative functional equations in the class of Lipschitz functions (Q1849464)

The authors study the question about Lipschitz solutions on convex compact subsets of \(\mathbb{R}^n\) of the iterative functional equation (IFE) \[ \sum^\ell_{i=1} a_if^i(x)= F(x),\quad F\text{ given}, \] where \(\ell\) can be \(\infty\). They prove a direct application of Schauder's fixed point theorem which offers ``a simple, elegant and general method in showing the existence of solutions of the IFE''.