Nonlinear mixed bi-skew Jordan-type derivations on prime *-algebras

Let A be a unite prime *-algebra containing a non-trivial projection. Assume that phi:A -> A satisfies phi(A(1) lozenge(1) A(2) lozenge(2)center dot center dot center dot lozenge(n) A(n+1)) = Sigma(n+1)(h=1) A(1) lozenge(1)center dot center dot center dot lozenge(h-2) A(h-1)lozenge(h-1) phi(A(h))lozenge(h) A(h+1)lozenge(h+1) center dot center dot center dot lozenge(n) A(n+1) (n >= 2) for any A(1), A(2),center dot center dot center dot,A(n+1)is an element of A and lozenge(r) is center dot or circle with 1 <= r <= n, where A center dot B = AB* + BA* and A circle B = AB + BA. In this article, we prove that ifnis even and lozenge(2u-1) = center dot, lozenge(2u) = degrees with 1 <= u <= n/2, then there exists an element lambda is an element of Z(S)(A) such that phi(A) = delta(A) + i lambda A, where delta is an additive *-derivation. Otherwise, phi is an additive *-derivation. In particular, the nonlinear mixed bi-skew Jordan-type derivations on factor von Neumann algebras and standard operator algebras are characterized.