Hyers-Ulam-Rassias Approximation on m-Lie

Using the xed point method, we establish the stability of m??Lie homomorphisms and Jordan m??Lie homomorphisms on m??Lie algebras associated to the following additive functional equation 2f Xm i=1 mxi ! = Xm i=1 f 0 @ 0 @mxi + Xm j=1 ;i6=j xj 1 A 1 A + f Xm i=1 xi ! where m is an integer greater than 2 and all  2 T 1 n0 := n ei ; 0    2 n0 o .