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

Subject Areas : Fixed point theory

M. Eshaghi Gordji ¹ , S. Abbaszadeh ²

1 - Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2 - Department of Mathematics, Payame Noor University, P.O. BOX 19395-4697, Tehran, Iran

Received: 2017-10-03 Accepted : 2017-12-10 Published : 2017-12-01

Keywords: Fixed point theorem, $2$-normed algebras, hyperstability, $(\alpha, \beta, \gamma)$-derivations,

Abstract :

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.

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