Homomorphisms in C∗C∗-ternary algebras and JB∗JB∗-triples

In this paper, we investigate homomorphisms between C∗C∗-ternary algebras and derivations on C∗C∗-ternary algebras, and homomorphisms between JB∗JB∗-triples and derivations on JB∗JB∗-triples, associated with the following Apollonius type additive functional equationf(z−x)+f(z−y)=−12f(x+y)+2f(z−x+y4).