On Certain Functional Equation in Semiprime Rings

Abstract

Let n be a fixed integer, let R be an (n+1)!-torsion free semiprime ring with the identity element and let F: R → R be an additive mapping satisfying the relation [Formula: see text] for all x ∈ R. In this case, we prove that F is of the form 2F(x)=D(x)+ax+xa for all x ∈ R, where D: R → R is a derivation and a ∈ R is some fixed element.