Characterization of non-linear mixed bi-skew Jordan triple higher derivations on prime *-algebras

Let A be aprime *-algebra. For any A, B ? A, define a new product A ? B = AB* + BA*. Let ? be a non-linear map satisfying ?(A ? B ? C) = ?(A) ? B ? C + A ? ?(B) ? C + A ? B ? ?(C) for all A, B, C ? A. In this article, we show that ? is an additive *-derivation. Furthermore, we also discuss above result for higher derivable maps on A.