Characterization of Non-Linear Bi-Skew Jordan n-Derivations on Prime *-Algebras

Let A be a prime *-algebra. A product defined as U center dot V = UV* + VU* for any U, V is an element of U, is called a bi-skew Jordan product. A map xi : U -> U, defined as x xi(p(n) (U-1, U-2,..., U-n)) = Sigma(n)(k=1) p(n)(U-1, U-2,..., U-k 1, xi(U-k), Uk+1,..., U-n) for all U-1, U-2,..., U-n is an element of U, is called a non-linear biskew Jordan n-derivation. In this article, it is shown that xi is an additive *-derivation.