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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 .

Jordan Triple Higher (Ïƒ,Ï„)-Homomorphisms on Prime Rings