b-Generalized derivations act as a multipliers on prime rings

Let R be a prime ring of characteristic different from 2, U be its Utumi quotient ring with the extended centroid C and f(x1,…,xn) be a non-central multilinear polynomial over C. Suppose that F, G and H are b-generalized derivations on R such that F(f(r))f(r)−f(r)G(f(r))=H(f(r)2) for all r∈Rn, then we describe all possible forms of F, G and H.