The author of the present pleasant paper establishes that if is a subalgebra of a Banach algebra and satisfies and , for all and for some , then there exists a unique additive derivation such that , and . The result and its proof are still true for a more general case if we consider a normed algebra and replace by a Banach -bimodule .
He also proves that if is a normed algebra with an identity belonging to , then every mapping satisfying must fulfil . This superstability result is nice, since there is not assumed any (approximately) additive condition on . Some similar results in which one considers generalized derivations can be found in the reviewer’s paper [“Hyers-Ulam-Rassias stability of generalized derivations”, Int. J. Math. Math. Sci. (to appear)].