Nonlinear Mixed bi-Skew Jordan-Type and Skew Jordan Higher Derivations on -Algebras*

Let A be a unital *-algebra over the complex field C, and let Ψ=ψmm∈N be a nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivation satisfies the relation ψm (L1⋄L2⋄…⋄Ln−1•Ln) =∑r1+…+rn=mψr1 (L1) ⋄…⋄ψrn−1 (Ln−1) •ψrn (Ln), where L•N=LN+NL* and L⋄N=L*N+N*L for all L, N, Li∈A with i∈1, 2, …, n. We demonstrate that every such higher derivation Ψ=ψmm∈N is an additive higher *-derivation. As an application, we use this result to characterize the structure of nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivations on a class of typical unital *-algebras, including standard operator algebras and von Neumann factors. This result also generalizes several existing results, in particular those concerning nonlinear mixed bi-skew Jordan-type and skew Jordan derivations on unital *-algebras.