Stability of Cubic Functional Equation in Three Variables (Communications in Mathematical Research, 2021)
In this paper, we prove a generalization of Hyers' theorem on the stability of approximately additive mapping and a generalization of Badora's theoremon approximate ring homomorphism. We also obtain more general stability theorem,which gives stability theorems on Jordan and Lie homomorphisms. The proofs of thetheorems in this paper are given following essentially the Hyers-Rassias approach tothe stability of the functional equations connected with Ulam's problem.
Keywords: stability; functional equation; Lie homomorphism.