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

Abstract

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 2 f(x1 + x2, y1 + y2, z1 + z2) = X f(xi, yj, zk). (1) i,j,k=1 Further, we investigate isomorphisms between complex ternary algebras, associated with the 3-additive functional equation.