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Analysis shows that nonlinear mixed bi-skew Jordan n-derivation is additive in von Neumann algebra, indicating its significance in algebraic structures.
Let A be a unital ∗-algebra over the complex fields C. In this article, it is proved that a nonlinear mixed bi-skew Jordan n-derivation is an additive ∗-derivation under certain conditions. As applications, the main result is applied to some special classes of ∗-algebras such as prime ∗-algebra, standard operator algebra, factor von Neumann algebra and von Neumann algebra with no central summands of type I1.
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Muzibur Rahman Mozumder (2025) studied this question.
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