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Iterative functional equations in the class of Lipschitz functions. (English) Zbl 1009.39021
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”.

##### MSC:
 39B12 Iteration theory, iterative and composite equations
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