Jordan Ѳ-Centralizers of Prime and Semiprime Rings

The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: RR an additive mapping such that T is left (right) Jordan Ѳ-centralizers on R. Then T is a left (right) Ѳ- centralizer of R, if one of the following conditions hold (i) R is a semiprime ring has a commutator which is not a zero divisor . (ii) R is a non commutative prime ring . (iii) R is a commutative semiprime ring, where Ѳ be surjective endomorphism of R . It is also proved that if T(xoy)=T(x)oѲ(y)=Ѳ(x)oT(y) for all x, y ϵ R and Ѳ-centralizers of R coincide under same condition and Ѳ(Z(R)) = Z(R) .