Stability of normal regions for linear homogeneous functional equations
type: Item
instance of: scholarly article
title: Stability of normal regions for linear homogeneous functional equations
zbMATH Open document ID: 0664.39003
DOI: 10.1007/BF01836089
author: Marek Czerni
published in: Aequationes Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137282
review text: The solution of the functional equation (1) \(\phi [f(x)]=g(x)\phi (x)\) is known to depend on an arbitrary function \(\phi_ 0(x)\) if certain simple conditions on f and g are satisfied. Starting from the notion of set stability for difference equations, introduced by \textit{G. A. Shanholt} [Int. J. Control, I. Ser. 19, 309-314 (1974; Zbl 0291.93036)], the author defines stability in the context of (1) and proceeds to give a number of results on stability, in particular also about continuous dependence on initial conditions.
Mathematics Subject Classification ID: 39B12
zbMATH DE Number: 4086212
zbMATH Keywords: linear functional equation
zbMATH Keywords: set stability
zbMATH Keywords: continuous dependence
MaRDI profile type: Publication
cites work: Q4191041
cites work: Q5592596
cites work: Set stability for difference equations
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description: scientific article; zbMATH DE number 4086212