Further results on stability of normal regions for linear homogeneous functional equations
type: Item
instance of: scholarly article
title: Further results on stability of normal regions for linear homogeneous functional equations
zbMATH Open document ID: 0826.39004
DOI: 10.1007/BF01827925
published in: Aequationes Mathematicae
publication date: 1995-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/182468
review text: This is a continuation of the author's paper [ibid. 36, No. 2/3, 176-187 (1988; Zbl 0664.39003)]. Regions are determined by solutions \(\psi : (0,a) \to \mathbb{R}\) to the inequality \(\psi (f(x)) \leq g(x) \psi (x)\), and stability of such a region with respect to the family of continuous solutions \(\varphi : (0,a) \to \mathbb{R}\) of the equation (1) \(\varphi (f(x)) = g(x) \varphi (x)\) is considered (the notion of set stability being adapted from that introduced for difference equations by E. Shanholt). The paper contains a necessary and sufficient condition for instability of a region and some sufficient conditions for its stability (the main results, according to the author's claim) in case the continuous solutions to (1) do not depend continuously on the initial conditions.
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39B72
zbMATH DE Number: 729142
zbMATH Keywords: stability of normal regions
zbMATH Keywords: linear homogeneous functional equations
zbMATH Keywords: iterative functional equations and inequalities
zbMATH Keywords: continuous solutions
zbMATH Keywords: set stability
zbMATH Keywords: instability
author: Marek Czerni
reviewed by: Bogdan A. Choczewski
MaRDI profile type: Publication
cites work: Q4191041
cites work: Stability of normal regions for linear homogeneous functional equations
cites work: Q5592596
description: scientific article; zbMATH DE number 729142