In this paper, the concept of Jordan triple higher -homomorphisms on prime rings is introduced.  A result of Herstein is extended on this concept from the ring  into the prime ring .  We prove that every Jordan triple higher -homomorphism of ring  into prime ring  is either triple higher -homomorphism  or triple higher -anti-homomorphism of  into .

In this paper, we will study some important results relating to the concept of generalized derivation in centrally prime ring to be commutative.

We will primarily extend the result of Herstein on it. It should be proved that every GJT()-HH of ring into prime ring is either GT()-HH or triple () higher antihomomorphism (T()-HAH).