Theoretical analysis reveals that nonlinear mixed bi-skew Jordan-Lie-type maps act as additive higher star-derivations, clarifying operator structures in von Neumann algebras.
Let [Formula: see text] be a unital ∗-algebra containing the nontrivial idempotents, and let [Formula: see text] be a family of nonlinear maps satisfying [Formula: see text] where [Formula: see text] and [Formula: see text] for all [Formula: see text] and [Formula: see text]. In this article, we prove that [Formula: see text] is an additive higher ∗-derivation. As applications, nonlinear mixed bi-skew Jordan-Lie-type higher derivations on prime ∗-algebras, factor von Neumann algebras and standard operator algebras are characterized.
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Liang et al. (2026) studied this question.
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