On a Functional Equation Related to Jordan Triple Derivations in Prime Rings

摘要

A classical result of Herstein asserts that any Jordan derivation on a prime ring with char( R ) ≠ 2 is a derivation. It is our aim in this paper to prove the following result, which is in the spirit of Herstein’s theorem. Let R be a prime ring with char( R ) = 0 or char( R ) > 4, and let D : R → R be an additive mapping satisfying the relation D ( x _(4)) = D ( x ) x _(3)+ xD ( x _(2)) x + x _(3) D ( x ) for all x ∈ R . In this case, D is a derivation.