Hyers-Ulam stability of functional equations in several variables
type: Item
instance of: scholarly article
title: Hyers-Ulam stability of functional equations in several variables
zbMATH Open document ID: 0836.39007
DOI: 10.1007/BF01831117
author: Gian Luigi Forti
published in: Aequationes Mathematicae
publication date: 1996-05-08T00:00:00Z
full work available at URL: https://eudml.org/doc/137624
review text: This is a survey about Hyers-Ulam stability of functional equations and systems in several variables. Except for the historical background the paper contains results on the stability of Cauchy, Jensen, quadratic and polynomial equations. The author presents superstability results concerning the multiplicative Cauchy equation and some cosine and sine functional equations. Further, approximately multiplicative linear maps in Banach algebras are considered. Moreover, the stability and the superstability of other equations and systems are discussed. Some final remarks and open problems end the paper. The bibliography contains 120 items.
Mathematics Subject Classification ID: 39B62
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 39-00
Mathematics Subject Classification ID: 39-03
zbMATH DE Number: 794227
zbMATH Keywords: historical survey
zbMATH Keywords: Cauchy functional equation
zbMATH Keywords: Jensen functional equation
zbMATH Keywords: quadratic functional equation
zbMATH Keywords: polynomial functional equation
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: functional equations
zbMATH Keywords: systems
zbMATH Keywords: superstability
zbMATH Keywords: cosine and sine functional equations
zbMATH Keywords: Banach algebras
zbMATH Keywords: bibliography
reviewed by: Andrzej Smajdor
MaRDI profile type: Publication
cites work: On the stability of a functional equation related to associativity
cites work: On some generalized invariant means and their application to the stability of the Hyers-Ulam type
cites work: The Stability of the Cosine Equation
cites work: The Stability of the Equation f(x + y) = f(x)f(y)
cites work: The Stability of a Functional Analogue of the Wave Equation
cites work: On Hyers-Ulam stability of Hosszú's functional equation
cites work: On a general Hyers-Ulam stability result
cites work: Approximately isometric and multiplicative transformations on continuous function rings
cites work: Classes of transformations and bordering transformations
cites work: Polynomial Approximations To Functions with Bounded Differences
cites work: The stability problem for transformations of the circle
cites work: On approximate solutions of the Pexider equation
cites work: The Stability of the Sine Equation
cites work: Remarks on the stability of functional equations
cites work: Q3343086
cites work: On the stability of the quadratic mapping in normed spaces
cites work: Représentations approchees d'un groupe dans une algèbre de Banach
cites work: A representation theorem for $(X_1-1)(X_2-1)...(X_n-1)$ and its applications
cites work: Q3732862
cites work: Q3831490
cites work: Q3976109
cites work: On the stability of a system of functional equations characterizing generalized hyperbolic and trigonometric functions
cites work: Q3884539
cites work: The stability of homomorphisms and amenability, with applications to functional equations
cites work: Sulla stabilita' degli omomorfismi e sue applicazioni alle equazioni funzionali
cites work: Q3473575
cites work: On stability of the Cauchy equation on semigroups
cites work: Local stability of the functional equation characterizing polynomial functions
cites work: On stability of additive mappings
cites work: Q4693726
cites work: Q4026437
cites work: Boundedness and continuity of additive and convex functionals
cites work: Q4272725
cites work: Q5562332
cites work: On the Stability of the Linear Functional Equation
cites work: Transformations with bounded \(m\)-th differences
cites work: Approximate homomorphisms
cites work: On the Hyers-Ulam stability of \(\psi\)-additive mappings
cites work: Perturbations of Banach algebras
cites work: Approximately Multiplicative Functionals
cites work: Approximately Multiplicative Maps Between Banach Algebras
cites work: On \(\varepsilon\)-representations
cites work: On a Local Stability of the Jensen Functional Equation
cites work: The stability of multiplicative semigroup homomorphisms to real normed algebras.
cites work: Sur la stabilité de l'équation d'homomorphisme
cites work: Q3800472
cites work: Q4007779
cites work: Q3897429
cites work: On approximation of approximately linear mappings by linear mappings
cites work: Q3733629

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q3721188

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Solution of a problem of Ulam

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q4697104

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: On the Stability of the Linear Mapping in Banach Spaces

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: On the stability of mappings

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: On a modified Hyers-Ulam sequence

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: On the Behavior of Mappings which do not Satisfy Hyers-Ulam Stability

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: On the Hyers-Ulam stability of linear mappings

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q4879438

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Isomorphisms of Standard Operator Algebras

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: The functional equation of multiplicative derivation is superstable on standard operator algebras

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Roots of formal power series in one variable

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Note on a problem in number theory

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q3957353

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Quasirepresentations and pseudorepresentations

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Proprieta’ locali e approssimazione di operatori

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Additive selections of superadditive set-valued functions

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: On a Theorem of Baker, Lawrence and Zorzitto

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q3665576

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Note on a Stability Theorem

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q3742042

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q3762999

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Fréchet's equation and Hyers theorem on noncommutative semigroups

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Stability of some functional equations in economics

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: An abstract superstability theorem

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Stability properties of functional equations describing the scientific laws

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: The Stability of the Sine and Cosine Functional Equations

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q4883956

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: On functions behaving like additive functions

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Quasi-additive functions

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q4012621

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q3293254

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: Q3221911

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: On functions with bounded \(n\)-th differences

Hyers-Ulam stability of functional equations in several variables (cites work)
cites work: On Bounded Functions with Bounded nth Differences

Hyers-Ulam stability of functional equations in several variables (OpenAlex ID)
OpenAlex ID: W1993677455

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: Hyers-Ulam stability of a functional equation with several parameters
Similarity Score: 0.9739218
Recommender Run: Recommender Run 3

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: Q4378545
Similarity Score: 0.9727055
Recommender Run: Recommender Run 3

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: Q3434001
Similarity Score: 0.96975493
Recommender Run: Recommender Run 3

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: Q5710323
Similarity Score: 0.96604437
Recommender Run: Recommender Run 3

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: On Hyers-Ulam-Rassias stability of functional equations
Similarity Score: 0.96568614
Recommender Run: Recommender Run 3

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: On the Hyers-Ulam-Rassias stability of functional equations in \(n\)-variables
Similarity Score: 0.9656379
Recommender Run: Recommender Run 3

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: On Hyers-Ulam stability for a class of functional equations
Similarity Score: 0.965124
Recommender Run: Recommender Run 3

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: Hyers-Ulam-Rassias stability of functional equations in mathematical analysis
Similarity Score: 0.9648279
Recommender Run: Recommender Run 3

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: Q4987532
Similarity Score: 0.9646346
Recommender Run: Recommender Run 3

Hyers-Ulam stability of functional equations in several variables (Recommended article)
Recommended article: Q3005289
Similarity Score: 0.9646201
Recommender Run: Recommender Run 3