×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI