Stability of Hyper 3-Homomorphisms and Hyper 3-Derivations in Ternary Algebras (European Journal of Pure and Applied Mathematics, 2025)
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.
Keywords: Hyers-Ulam stability; homomorphisms; derivations; ternary algebra