Stability of Functional Equations and Properties of Groups

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.

Keywords

• additive functional equation
• quadratic functional equation
• stability
• amenable group
• weak commutativity
• 39B82
• 20F12
• 43A07