Additivity of Multiplicative b-Generalized (Skew) Derivations

Let R be a prime ring and Q be the right Martindale quotient ring of R. Then we prove that a map G on R satisfies \(G(xy)=G(x)y+ b\alpha (x)d(y)\) for all \(x,y\in R\) where \(\alpha \) is an automorphism on R and d is an additive map over R, \(b \in Q\) , is additive. Moreover, if a map g on R satisfying \(g(xy)=g(x)y + bxd(y)\) for all \(x,y\in R\) and d, b are mentioned above, then g is additive.