Bourgin (DukeMath J 16:385–397, 1949) proved that every approximate ring homomorphism from a Banach algebra onto a unital Banach algebra is automatically a ring homomorphism. Martindale (Proc Am Math Soc 21:695–698, 1969) proved that every multiplicative isomorphism from a prime ring containing a nontrivial idempotent onto an arbitrary ring is automatically additive. We show these results for approximate multiplicative skew derivations and approximate skew derivations. Some closely related results are also discussed. Furthermore, we give some important consequences and illustrative examples from our main results
