On the stability of a generalized additive functional equation

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