Iterative functional equations in the class of Lipschitz functions
type: Item
instance of: scholarly article
title: Iterative functional equations in the class of Lipschitz functions
zbMATH Open document ID: 1009.39021
author: Marcin Kulczycki
author: Jacek Tabor
published in: Aequationes Mathematicae
publication date: 2002-12-01T00:00:00Z
review text: 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''.
reviewed by: Borislav Crstici
Mathematics Subject Classification ID: 39B12
zbMATH DE Number: 1837091
zbMATH Keywords: itrative functional equations
zbMATH Keywords: Lipschitz functions
zbMATH Keywords: ideally convex set
zbMATH Keywords: Cauchy functional equation
MaRDI profile type: Publication
full work available at URL: s00010-002-8028-2
OpenAlex ID: W2114022925
Wikidata QID: Q112226164
DOI: 10.1007/S00010-002-8028-2
description: scientific article; zbMATH DE number 1837091