Abstract
The aim of the paper is to give a description of nonlinear Jordan derivable mappings of a certain class of generalized matrix algebras by Lie product square-zero elements. We prove that under certain conditions, a nonlinear Jordan derivable mapping Δ of a generalized matrix algebra by Lie product square-zero elements is a sum of an additive derivation δ and an additive antiderivation f . Moreover, δ and f are uniquely determined.
Highlights
For all A, B ∈ A with [A, B] ∈ Ω, we say Δ is a nonlinear Jordan derivable mapping of A by Lie product square-zero elements
We prove that under certain conditions, a nonlinear Jordan derivable mapping Δ of a generalized matrix algebra by Lie product square-zero elements is a sum of an additive derivation δ and an additive antiderivation f
Ashraf and Jabeen in [11] showed that every nonlinear Jordan triple derivable mapping on a 2-torsion Journal of Mathematics free triangular algebra is an additive derivation
Summary
For all A, B ∈ A with [A, B] ∈ Ω, we say Δ is a nonlinear Jordan derivable mapping of A by Lie product square-zero elements. Let G be a 2-torsion free generalized matrix algebra and Δ be a nonlinear Jordan derivable mapping of G by Lie product square-zero elements.
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