Abstract
Let R be a ring. An additive mapping f : R -> R is called 3-homomorphism (resp. 3-antihomomorphsm) on R if f(xyz) = f(x) f(y) f(z) (resp. f(xyz) = f(z) f(y) f(x)) for all x, y, z is an element of R. In the present paper, we characterize multiplicative (generalized)-derivation which acts as a 3-homomorphism or as a 3-antihomorphism on an appropriate subset of a ring R.