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={ψm}m∈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={ψm}m∈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.