Let Formula: see text be a Formula: see text-torsion free unital *-ring, possessing a non-trivial symmetric idempotent. In the present paper, we discuss that, under certain mild conditions on Formula: see text, a map Formula: see text : Formula: see text (not necessarily additive) satisfies Formula: see text for all Formula: see text if and only if it is an additive *-derivation. Furthermore, we discuss our main result to certain classes of *-algebras like as prime *-algebra, von Neumann algebras without central summands of type Formula: see text and standard operator algebras.
Siddeeque et al. (Fri,) studied this question.