  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.
