# zbMATH — the first resource for mathematics

Let $$(S,\cdot)$$ be a semigroup, $$f: S\to\mathbb{R}$$ a subadditive functional, $$g: S\to\mathbb{R}$$ a superadditive functional and assume $$g(x)\leq f(x)$$ for all $$x\in S$$. The authors deal with the problem of separating $$g$$ and $$f$$ by means of an additive functional. They obtain results when $$S$$ is weakly commutative (i.e. $$\forall x,y\in S$$ $$\exists n\in\mathbb{N}$$: $$(xy)^{2n}=x^{2n}y^{2n})$$ and/or is amenable. Some of the results are related to Hyers-Ulam stability of the Cauchy equation.