Multiplicative Lie triple higher derivations on generalized matrix algebras

Let N be the set of nonnegative integers and G = ( A , M , N , B ) be a 2-torsion free generalized matrix algebra over a commutative ring R . In the present paper, under some lenient assumptions on G , it is shown that if ∆ = { δ n } n ∈ N is a sequence of mappings δ n : G → G (not necessarily linear) satisfying δ n ([[ a,b ] ,c ]) = P r + s + t = n [[ δ r ( a ) ,δ s ( b )] ,δ t ( c )] for all a,b,c ∈ G , then for each n ∈ N , δ n = d n + τ n ; where d n : G → G is an additive mapping satisfying d n ( ab ) = P r + s = n d r ( a ) d s ( b ) for all a,b ∈ G , i.e., D = { d n } n ∈ N is an additive higher derivation on G and τ n : G → Z ( G )(where Z ( G ) is the center of G ) is a map vanishing at every second commutator [[ a,b ] ,c ].