Isometric isomorphisms in proper CQ*-algebras

In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ*-algebras for the following Cauchy-Jensen additive mapping: $$ 2f\left( {\frac{{x_1 + x_2 }} {2} + y} \right) = f(x_1 ) + f(x_2 ) + 2f(y). $$ The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias’ stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297–300.