b'-Generalized skew derivations acting as a Jordan derivation on multilinear polynomials in prime rings

Let R be a prime ring of characteristic not equal to 2, U the Utumi quotient ring of R, C the extended centroid of R and f(x(1),..., x(n)) a noncentral multi linear polynomial of R. Let F, H be b'-generalized skew derivations on R, with associated terms (b',alpha, d) and (b', alpha,delta) respectively, and alpha commutes with d and delta. In this article we study the complete structure of F and H in the case F(u)u + uF(u) = H(u(2)), for all u = f (r(1), ... , r(n)), r(1), r(2), ... , r(n) is an element of R.