<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Investigating Hyers–Ulam stability of the additive Cauchy equation with domain in a group <italic>G</italic>, in order to obtain an additive function approximating the given almost additive one we need some properties of <italic>G</italic>, 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.</p></abstract>

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.

Stability of Functional Equations and Properties of Groups

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"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...

Stability of Functional Equations and Properties of Groups

Published Online: Jul 18, 2019

Page range: 77 - 96

Received: Mar 18, 2019

Accepted: Apr 15, 2019

DOI: https://doi.org/10.2478/amsil-2019-0004

Keywords
additive functional equation, quadratic functional equation, stability, amenable group, weak commutativity

© 2019 Gian Luigi Forti, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Stability of Functional Equations and Properties of Groups

Published Online: Jul 18, 2019

Page range: 77 - 96

Received: Mar 18, 2019

Accepted: Apr 15, 2019

DOI: https://doi.org/10.2478/amsil-2019-0004

Keywordsadditive functional equation, quadratic functional equation, stability, amenable group, weak commutativity

© 2019 Gian Luigi Forti, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
additive functional equation, quadratic functional equation, stability, amenable group, weak commutativity