(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduce hyper 3-homomorphisms and hyper 3-derivations in complex ternary algebras and 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 eqnarray0.1 f(x_1+x_2,y_1+y_2,z_1+z_2)=_i,j,k=1^2 f(x_i,y_j,z_k). eqnarray Further, we investigate isomorphisms between complex ternary algebras, associated with the 3-additive functional equation.