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)=λ 3 D(a) for any complex number λ and all a∈A, and D(ab)=D(a)⋅b 3+a 3⋅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.
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The author sincerely thanks the anonymous referee for a careful reading, constructive comments and fruitful suggestions to improve the quality of the paper and suggesting a related reference.
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Bodaghi, A. Cubic derivations on Banach algebras. Acta Math Vietnam. 38, 517–528 (2013). https://doi.org/10.1007/s40306-013-0031-2
- Banach algebra
- Cubic derivation
Mathematics Subject Classification (2000)