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: f x + y 2 +z +f x −y 2 + z = f (x) +2f (z), (0.1) f x + y 2 +z −f x −y 2 + z = f (y), (0.2) 2f x + y 2 +z = f (x)+ f (y) +2f (z). (0.3) 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]. © 2006 Elsevier Inc. All rights reserved.