  A mapping $f:(G_1,[ ]_1)\to (G_2,[ ]_2)$ between ternary semigroups will be
called a ternary homomorphism if $f([xyz]_1)=[f(x)f(y)f(z)]_2$. In this paper,
we prove the generalized Hyers--Ulam--Rassias stability of mappings of
commutative semigroups into Banach spaces. In addition, we establish the
superstability of ternary homomorphisms into Banach algebras endowed with
multiplicative norms.
