Non-global nonlinear mixed skew Jordan Lie triple derivations on prime *-rings

Let R be a 2-torsion free unital prime *-ring containing a nontrivial symmetric idempotent and Zc(R) be the anti-symmetric center of R. We prove that if a map cc : R-R satisfies cc([A center dot B, C]) = [cc(A) center dot B, C] + [A center dot cc(B), C] + [A center dot B, cc(C)] for any A, B, C E R with ABC* = 0, then there exists an additive *-derivation Theta of R and a nonlinear map g : R-Zc(R) such that cc(A) = Theta(A) + g(A) for any A E R.