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

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.

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