Nonlinear Jordan Triple Higher Derivable Mappings of Triangular Algebras

Let A, B be unital R-algebras over a commutative ring R with unity andM be a nonzero (A, B)-bimodule which is faithful as a left A-module and also as a right B-module. Suppose that U = Tri(A, M, B) is a 2-torsion free triangular algebra consisting of A, B and M and N is the set of non-negative integers. In the present paper it is shown that if Delta = {delta(n)}(n is an element of N) is a sequence of mappings delta(n) : U -> U (not necessarily linear) such that delta(n)(XY Z + ZY X) = Sigma(i+j+k=n) (delta(i)(X)delta(j)(Y)delta(k)(Z)+delta(i)(Z)delta(j)(Y)delta(k)(X)) for all X, Y, Z is an element of U, then Delta = {delta(n)}(n is an element of N) is an additive higher derivation on U.