Stability of Functional Equations and Properties of Groups

Stability of Functional Equations and Properties of Groups

Investigating Hyers–Ulam stability of the additive Cauchy equation with domain in a group G, in order to obtain an additive function approximating the given almost additive one we need some properties of G, starting from commutativity to others more sophisticated. The aim of this survey is to presen...

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Bibliographic Details
Main Author: Forti Gian Luigi
Format: Article
Language:English
Published: Sciendo 2019-09-01
Series:Annales Mathematicae Silesianae
Subjects:
additive functional equation
quadratic functional equation
stability
amenable group
weak commutativity
39B82
20F12
43A07
Online Access:http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0004/amsil-2019-0004.xml?format=INT
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spelling doaj-b3f09c08a23c412b997116979fa433222020-11-24T21:24:08ZengSciendoAnnales Mathematicae Silesianae2391-42382019-09-01331779610.2478/amsil-2019-0004amsil-2019-0004Stability of Functional Equations and Properties of GroupsForti Gian Luigi0Università degli Studi di Milano, Dipartimento di Matematica, via C. Saldini 50, I-20133Milano, Italy; e-mail: gianluigi.forti@unimi.it;Investigating Hyers–Ulam stability of the additive Cauchy equation with domain in a group G, in order to obtain an additive function approximating the given almost additive one we need some properties of G, starting from commutativity to others more sophisticated. The aim of this survey is to present these properties and compare, as far as possible, the classes of groups involved.http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0004/amsil-2019-0004.xml?format=INTadditive functional equationquadratic functional equationstabilityamenable groupweak commutativity39B8220F1243A07
collection DOAJ
language English
format Article
sources DOAJ
author Forti Gian Luigi
spellingShingle Forti Gian Luigi
Stability of Functional Equations and Properties of Groups
Annales Mathematicae Silesianae
additive functional equation
quadratic functional equation
stability
amenable group
weak commutativity
39B82
20F12
43A07
author_facet Forti Gian Luigi
author_sort Forti Gian Luigi
title Stability of Functional Equations and Properties of Groups
title_short Stability of Functional Equations and Properties of Groups
title_full Stability of Functional Equations and Properties of Groups
title_fullStr Stability of Functional Equations and Properties of Groups
title_full_unstemmed Stability of Functional Equations and Properties of Groups
title_sort stability of functional equations and properties of groups
publisher Sciendo
series Annales Mathematicae Silesianae
issn 2391-4238
publishDate 2019-09-01
description Investigating Hyers–Ulam stability of the additive Cauchy equation with domain in a group G, in order to obtain an additive function approximating the given almost additive one we need some properties of G, starting from commutativity to others more sophisticated. The aim of this survey is to present these properties and compare, as far as possible, the classes of groups involved.
topic additive functional equation
quadratic functional equation
stability
amenable group
weak commutativity
39B82
20F12
43A07
url http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0004/amsil-2019-0004.xml?format=INT
work_keys_str_mv AT fortigianluigi stabilityoffunctionalequationsandpropertiesofgroups
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