n-Derivations of triangular algebras

Let A be a triangular algebra. Let n⩾2 be an integer. A map φ:A×A×⋯×A→A is said to be a n-derivation if it is a derivation in each argument. In this paper we investigate n-derivations (n⩾3) for a certain class of triangular algebras. The main result is then applied to upper triangular matrix algebras and nest algebras.