Some remarks on the stability of the Cauchy equation and completeness (Q2055265)

Let \(S\) be a commutative semigroup and \(X\) be a Banach space. It is well known that every function \(f:S\to X\) such that the norm of its Cauchy difference is bounded by a constant is close to some additive function. In this paper, the authors discuss the case when the bound is a suitable non-constant function. They also find some characterizations of completeness by stability in Archimedean and non-Archimedean spaces.