Stability of Functional Equations in Several Variables

Abstract

In this note, we prove a generalization of Hyers’ theorem on the stability of approximately additive mapping and a generalization of Badora’s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the 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 the stability of functional equations connected with S. M. Ulam’s problem.