On the stability of a generalized additive functional equation

We consider the Hyers–Ulam stability of a functional equation for continuous functions on a space on which a topological group acts, analogously to the additive functional equation on a group. We show, among other things, that our generalized additive equation, for continuous functions on a homogeneous space of a strongly amenable topological group, is stable provided that the canonical projection from that group to its homogeneous space is a fiber bundle.