Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201060420171201A fixed point method for proving the stability of ring $(alpha, beta, gamma)$-derivations in $2$-Banach algebras269276536116ENM. Eshaghi GordjiDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranS. AbbaszadehDepartment of Mathematics, Payame Noor University, P.O. BOX 19395-4697, Tehran, Iran0000-0002-8257-0116Journal Article20171003In 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.http://jlta.iauctb.ac.ir/article_536116_a2fa96c0595bab5c5faf576f3e547c7f.pdf