Key points are not available for this paper at this time.
Let Formula: see text be a ∗-algebra with unity Formula: see text and a nontrivial projection Formula: see text. In this paper, it is shown that if a map Formula: see text satisfies Formula: see text for all Formula: see text, Formula: see text, Formula: see text and Formula: see text for all Formula: see text, where Formula: see text, then Formula: see text is an additive ∗-derivation. Moreover, we shall call such a map Formula: see text, a nonlinear mixed ∗-Jordan Formula: see text-derivation. As applications, we will characterize nonlinear mixed ∗-Jordan Formula: see text-derivation in standard operator algebras and von Neumann algebras.
Siddeeque et al. (Thu,) studied this question.