Jordan derivations on $C^*$-ternary algebras for a Cauchy-Jensen functional equation

Abstract: In this paper, we proved the generalized Hyers-Ulam stability of homomorphisms in $C^*$- ternary algebras and of derivations on $C^*$-ternary algebras for the following Cauchy- Jensen functional equation $$3f\bigg(\frac{x+y+z}{3}\bigg)=2f\bigg(\frac{x+y}{2}\bigg)+f(z).$$ These were applied to investigate isomorphisms between $C^*$-ternary algebras.