On the superstability of a special derivation

Subject Areas : Functional analysis

M.  Hassani ¹ (Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad 91735, Iran)
E.  Keyhani ² (Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad 91735, Iran)

Received: 2014-05-14 Accepted : 2014-08-20 Published : 2014-03-01

Keywords: Stable, Superstable, Multiplicative Derivations, Ring $(alpha, beta)$, Linear $(alpha, beta)$-derivations, Multiplicative $(alpha, beta)$-derivations,

Abstract :

The aim of this paper is to show that under some mild conditions a functional equation of multiplicative $(\alpha,\beta)$-derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner $(\alpha,\beta)$-derivation.

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