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 ( x 2 ) = F ( x ) x ∗ + x D ( 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 ) = q x ∗ + 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.