Algebraic identities and generalized derivations in prime rings

Let R be a prime ring with center Z(R). A map F from R to R is called a multiplicative generalized derivation associated with d (not necessarily additive) if F(xy)= F(x)y + xd(y) for all x and y in R. In this paper, our intention is to study the commutativity of R, using a multiplicative generalized derivation that satisfies some algebraic identities.