Characterizations of generalized Lie n-higher derivations on certain triangular algebras

The aim of this paper was to provide a characterization of nonlinear generalized Lie $ n $-higher derivations for a certain class of triangular algebras. It was shown that, under some mild conditions, each component $ G_r $ of a nonlinear generalized Lie $ n $-higher derivation $ \{G_r\}_{r\in N} $ of the triangular algebra $ \mathcal{U} $ could be expressed as the sum of an additive generalized higher derivation and a nonlinear mapping vanishing on all ($ n-1 $)-th commutators on $ \mathcal{U} $.