Characteristic solutions of polynomial-like iterative equations
type: Item
instance of: scholarly article
title: Characteristic solutions of polynomial-like iterative equations
zbMATH Open document ID: 1060.39019
author: Dilian Yang
author: Weinian Zhang
published in: Aequationes Mathematicae
publication date: 2004-11-26T00:00:00Z
review text: This paper belongs to the class of iterative equations which are of special interest for people in dynamical systems and functional equation. Precisely, the authors deal with the polynomial-like iterative equation \[ f^n (x) = \sum_{j=0}^{n-1} a_j f^j (x) \] where \( a_0, a_1,\dots, a_{n-1} \) are real numbers. The case \( f(x) = rx \), \( x \in C\), with \(r\) as unknown, is studied with detail. Some previous results are extended and the case of multiple characteristic roots is faced. They describe such equation in linear difference form, give relations between the characteristic solutions and other solutions and they construct in specific cases all continuous solutions. It is shown that the equation has no continuous real solutions of it has no real characteristic roots.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 37E05
zbMATH DE Number: 2119227
zbMATH Keywords: iteration
zbMATH Keywords: characteristic solution
zbMATH Keywords: linear difference form
zbMATH Keywords: polynomial-like iterative equation
zbMATH Keywords: continuous solutions
MaRDI profile type: Publication
full work available at URL: s00010-003-2708-4
OpenAlex ID: W1976078904
DOI: 10.1007/S00010-003-2708-4
description: scientific article; zbMATH DE number 2119227