Identities involving generalized derivations act as Jordan homomorphisms

Let R be a prime ring with char( R ) is not equal to 2 and π ( ω 1 , … , ω n ) be a noncentral multilinear polynomial over the extended centroid C of R . If F 1 , F 2 and F 3 are generalized derivations on R such that F 1 ( F 3 ( ξ 2 ) ) = F 2 ( ξ ) F 3 ( ξ ) for all ξ = π ( ω 1 , … , ω n ) , ω 1 , … , ω n ∈ R , then we describe all possible forms of generalized derivations F 1 , F 2 and F 3 .