Acta Mathematica Vietnamica

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Cubic derivations on Banach algebras
Abasalt Bodaghi

 

Abstract

Let A be a Banach algebra and X be a Banach A-bimodule. A mapping D: AX 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 aA, and D(ab)=D(a)⋅b3+a3D(b) for all a,bA. 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.

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