  In this paper, using the fixed point and direct methods, we prove the
generalized Hyers-Ulam-Rassias stability of a Cauchy-Jensen additive functional
equation in various normed spaces. The concept of Hyers-Ulam-Rassias stability
originated from Th. M. Rassias stability theorem that appeared in his paper: On
the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72
(1978), 297-300.
