Stability of hyper homomorphisms and hyper derivations in complex Banach algebras

Abstract

<abstract><p>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:</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} g(x_1+x_2, y_1+y_2, z_1+z_2) = \sum\limits_{i, j, k = 1}^2 g(x_i, y_j, z_k). \end{align*} $\end{document} </tex-math></disp-formula></p> </abstract>