Isomorphisms between C-*-ternary algebras

Abstract

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 generalized Cauchy-Jensen additive mapping: 2f(Sigma(p)(j-1)x(j)/2 + Sigma(d)(j=1)y(i)) = Sigma(p)(j=1)f(x(j)) + 2 Sigma(d)(j=1)f(y(i))/ This is applied to investigate isomorphisms between C-*-ternary algebras. The concept of Hyers-Ulam-Rassias stability originated from the Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, see Proc. Amr. Math. Soc. 72, 297-300 (1978).