Constructive solutions for systems of iterative functional equations
type: Item
instance of: scholarly article
title: Constructive solutions for systems of iterative functional equations
zbMATH Open document ID: 1369.39019
author: Cristina Serpa
author: Jorge Buescu
published in: Constructive Approximation
publication date: 2017-05-02T00:00:00Z
review text: This comprehensive paper studies the systems of iterative functional equations. Generally, they are of the following form. Let \(X,Y\) be nonempty sets and \(p\geq2\) an integer. For \(X_i\subset X\), \(\bigcup_{i=0}^{p-1}X_i=X\), \(W_i\subset X\) and given functions \(f_i: X_i\to W_i\) and \(F_i: X_i\times Y\to Y\) (\(i=0,1,\dots,p-1\)) we consider the system of functional equations \[ \varphi(f_i(x))=F_i(x,\varphi(x)),\quad x\in X_i, \,i=0,1,\dots,p-1,\tag{\(*\)} \] with an unknown function \(\varphi: X\to Y\). The above system is considered with some ``compatibility conditions''. The first part of the paper is devoted to providing some necessary and sufficient conditions for the existence and uniqueness of the solutions of \((*)\), in the general case, as well as for the the existence of bounded and continuous solutions (under suitable additional assumptions upon \(X\) and \(Y\)). Later, the authors consider some particular cases, with respect to the type of the functions \(f_i\) and \(F_i\). Finally, some applications are given including some earlier results covered by the general results presented in the considered paper.
reviewed by: Jacek Chmieliński
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39B72
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 6710483
zbMATH Keywords: explicit solutions
zbMATH Keywords: De Rham function
zbMATH Keywords: fractal interpolation
zbMATH Keywords: iterative functional equations
zbMATH Keywords: system of functional equations
zbMATH Keywords: bounded and continuous solutions
MaRDI profile type: Publication
full work available at URL: s00365-016-9349-z
OpenAlex ID: W2460046084
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DOI: 10.1007/S00365-016-9349-Z
description: scientific article; zbMATH DE number 6710483