A Note on Generalized Jordan *-Derivations on Prime *-Rings

Let R be an associative ring with involution ∗. In this paper, we study an additive mapping F : R → R, namely generalized Jordan ∗-derivation, satisfying F(x2) = F(x)x∗ + xD(x) for any x ∈ R associated with a Jordan ∗-derivation D on R. It is shown that, in case R as a prime ∗-ring with char(R) ≠ 2, F is of the form F(x) = qx∗ + D(x) for any x ∈ R. In the spirit of this result, we discuss the celebrated Posner’s [27] second theorem and other results in the setting of generalized Jordan ∗-derivations.