Identities involving b-generalized skew derivations in prime rings acting as Jordan derivation

Let R symbolize a prime ring with a characteristic other than 2, and let rho(eta(1 ), & mldr; , eta(n)) represent a non-central multilinear polynomial over the extended centroid C of R . Assuming the presence of three b-generalized skew derivations on R , namely D-1, D-2 , and D(3 )that satisfy the equation D-1(rho)rho + rho D-2(rho) = D-3(rho(2)) for all rho=rho(eta(1 ),& mldr; , eta(n)) , where eta(1 ), & mldr; , eta(n )are elements of R . In this research paper, our goal is to elucidate all potential configurations of D-1, D-2 , and D-3.