Cubic derivations on Banach algebras
Abasalt Bodaghi

Abstract

Let A be a Banach algebra and X be a Banach A-bimodule. A mapping D: A⟶X is a cubic derivation if D is a cubic homogeneous mapping, that is, D is cubic and D(λa)=λ³D(a) for any complex number λ and all a∈A, and D(ab)=D(a)⋅b³+a³⋅D(b) for all a,b∈A. In this paper, we prove the stability of a cubic derivation with direct method. We also employ a fixed point method to establish the stability and the superstability of cubic derivations.