b -generalized skew derivations acting on multilinear polynomials in prime rings

Let R be a prime ring of characteristic not equal to 2, Z(R) its center, Qr its right Martindale quotient ring, C its extended centroid, f(x1,…,xn)a non-central multilinear polynomial over C and u,v∈Qr. Suppose that F and H are two b-generalized skew derivations of R with associated terms (b,α,d) and (b,α,δ). In this article we study the complete structure of F and H satisfying uF(f(X))f(X)+F(f(X))f(X)v=H(f(X)2) for any X=(r1,…,rn)∈Rn.