A fixed point method for proving the stability of ring $(alpha, beta, gamma)$-derivations in $2$-Banach algebras

In this paper, we first present the new concept of $2$-normed algebra. We investigate the structure of this algebra and give some examples. Then we apply a fixed point theorem to prove the stability and hyperstability of $(alpha, beta, gamma)$-derivations in $2$-Banach algebras.