On the Hahn-Banach theorem for groups

Abstract.

Let $\mathcal{G}$ be the family of all groups such that under each subadditive functional there exists an additive functional. We show that the class $\mathcal{G}$ is between the class of all amenable groups and the family of all groups for which the Hyers stability theorem for homomorphisms holds true. Next, we generalize the classical Hahn-Banach theorem to the class $\mathcal{G}$ .