Stability of group and ring homomorphisms

In this paper, we give generalization of Hyers' theorem on the stability of approximately additive mapping and a generalization of Badora's theorem on approximate ring homomorphism. We also obtain a more general stability theorem, which gives stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers - Th. M. Rassias approach to stability of functional equations connected with S. M. Ulam's problem.