Stability of hyper homomorphisms and hyper derivations in complex Banach algebras

In this paper, we introduce the concept of hyper homomorphisms and hyper derivations in Banach algebras and we establish the stability of hyper homomorphisms and hyper derivations in Banach algebras for the following 3-additive functional equation: g(x(1) + x(2), y(1) + y(2),z(1) + z(2)) = Sigma(2)(i,j,k=1) g(x(i), y(j), z(k)).

Automated summary

This paper introduces the concepts of hyper homomorphisms and hyper derivations in Banach algebras, and establishes their stability in a specific functional equation.