Let H be a real or complex Hilbert space with dim(H) > 1, B(H) be algebra of all bounded linear operators on H and A(H) ⊆ B(H) be a standard operator algebra on H . If D : A(H) → B(H) is a linear mapping satisfying D(An+1) = n∑ i=0 AiD(A)(A∗)n−i for all A ∈ A(H), then D is a Jordan ∗-derivation on A(H). Later, we discuss some algebraic identities on semiprime rings.