Isomorphisms between C∗-ternary algebras

In this paper, we prove the Hyers–Ulam–Rassias stability of homomorphisms in C∗-ternary algebras and of derivations on C∗-ternary algebras for the following Cauchy–Jensen additive mappings:equation(0.1)f(x+y2+z)+f(x−y2+z)=f(x)+2f(z),equation(0.2)f(x+y2+z)−f(x−y2+z)=f(y),equation(0.3)2f(x+y2+z)=f(x)+f(y)+2f(z). These are applied to investigate isomorphisms between C∗-ternary algebras. The concept of Hyers–Ulam–Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297–300].