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

Kulczycki, Marcin; Tabor, Jacek

Aequationes Math. 64, No. 1-2, 24-33 (2002).

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”.

Reviewer: Borislav Crstici (Timişoara)

MSC:

39B12

Iteration theory, iterative and composite equations

Keywords:

itrative functional equations; Lipschitz functions; ideally convex set; Cauchy functional equation