Stability of homomorphisms and derivations in $C^{\ast }$-ternary algebras

Abstract

In this paper, we investigate homomorphisms between $C^{\ast }$-ternary algebras and derivations on $C^{\ast }$-ternary algebras, associated with the following functional equation $$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3x_3}{3})+f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$ Moreover, we prove the generalized Hyers-Ulam -Rassias stability of homomorphisms in $C^{\ast }$-ternary algebras and of derivations on $C^{\ast }$-ternary algebras.

Cited by in corpus (1)

• Jordan derivations on $C^{\ast }$-ternary algebras for a Cauchy-Jensen functional equation