b-Generalized Derivations Acting on Multilinear Polynomials in Prime Rings

Let R be a prime ring of characteristic different from 2, Q be its maximal right ring of quotients, and C be its extended centroid. Suppose that $f(x_1,\dots ,x_n)$ is a non-central multilinear polynomial over C, $0\ne p\in R$, and F, G are two b-generalized derivations of R. In this paper we describe all possible forms of F and G in the case $pG(F(f(r))f(r))=0$ for all $r=(r_1,\dots ,r_n)$ in Rⁿ.