Note on nonstability of the linear functional equation of higher order

We provide a complete solution of the problem of Hyers–Ulam stability for a large class of higher order linear functional equations in single variable, with constant coefficients. We obtain this by showing that such an equation is nonstable in the case where at least one of the roots of the characte...

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Vydané v:Computers & mathematics with applications (1987) Ročník 62; číslo 6; s. 2648 - 2657
Hlavní autori: Brzdȩk, Janusz, Popa, Dorian, Xu, Bing
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Ltd 01.09.2011
Predmet:
Approximation
Chaos theory
Characteristic root
Dynamical systems
Hyers–Ulam stability
Linear equation
Mathematical analysis
Mathematical models
Modules
Nonstability
Normed space
Roots
Stability
Characteristic root
Normed space
Linear equation
Nonstability
Hyers–Ulam stability
ISSN:0898-1221, 1873-7668
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Popis
Shrnutí:We provide a complete solution of the problem of Hyers–Ulam stability for a large class of higher order linear functional equations in single variable, with constant coefficients. We obtain this by showing that such an equation is nonstable in the case where at least one of the roots of the characteristic equation is of module 1. Our results are related to the notions of shadowing (in dynamical systems and computer science) and controlled chaos. They also correspond to some earlier results on approximate solutions of functional equations in single variable.
Bibliografia:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2011.08.007