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

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