Higher derivations on Lie ideals of triangular algebras

Let $\mathscr T$ be a triangular algebra and let $\mathscr U$ be an admissible Lie ideal of $\mathscr T$. We mainly consider the question whether each Jordan higher derivation of $\mathscr U$ into $\mathscr T$ is a higher derivation of $\mathscr U$ into $\mathscr T$. We also give some characterizations for the Jordan triple higher derivations of $\mathscr U$.