Assume N be a -ring with N be a Ѓ-ring. In the presented paper introduced the concept of generalized (,)-khomomorphism , generalized Jordan (,)-k-homomorphism, generalized Jordan triple (,)-k-homomorphismgeneralized(,)-k–anti homomorphism with show that under certain conditions of N, any generalized Jordan (,)-k-homomorphism F from a -ring N into a two-torsion free Ѓ -ring N, such that wrw = wrw, for any w, r  N with,   , w''r''w' = w''r''w', for any w', r'  Ń with ', ' Ѓ , 2 = , 2 =  with  = , then D is a generalizedJordan triple (,)-k-homomorphism.