investigation hyers-ulam stability of hyper 3-homomorphisms and hyper 3-derivations in complex ternary algebras

In this work, we study the notions of hyper 3-homomorphisms and hyper 3- derivations in the framework of complex ternary algebras. we establish the hyers–ulam stability results for these mappings corresponding to the following 3-additive functional equation: (1) f(x1 + x2, y1 + y2, z1 + z2) = 2∑ i,j,k=1 f(xi, yj, zk). in addition, we examine the structure of isomorphisms between complex ternary algebras that are related to the above 3-additive functional equation.