The main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe Pexiderized exponential equation, i.e., where , and are three functions from an arbitrarycommutative semigroup to an arbitrary unitary complex Banachalgebra and also is afunction. Furthermore, in connection with the open problem of Th.M. Rassias and our results we generalized the theorem of Baker,Lawrence, Zorzitto and theorem of L. Szkelyhidi.
