Stability of Hyper 3-Homomorphisms and Hyper 3-Derivations in Ternary Algebras

In this paper, we introduce hyper 3-homomorphisms and hyper 3-derivations in complex ternary algebrasand we prove the Hyers-Ulam stability of hyper 3-homomorphisms and hyper 3-derivations in complex ternary algebras for the following 3-additive functional equation \begin{eqnarray}\label{0.1} f(x_1+x_2,y_1+y_2,z_1+z_2)=\sum_{i,j,k=1}^{2} f(x_i,y_j,z_k).\end{eqnarray}Further, we investigate isomorphisms between complex ternary algebras, associated with the 3-additive functional equation.