Characterization of Generalized Jordan Higher Derivations on Triangular rings

Let $\mathcal{A}$ and $\mathcal{B}$ be unital rings and $\mathcal{M}$ be a $(\mathcal{A},\mathcal{B})$-bimodule, which is faithful as a left $\mathcal A$-moduleandalsoasaright$\mathcal B$-module\mathrm{.}Let${\mathcal U}={\rm Tri}(\mathcal A, \mathcal M, \mathcal B)$ be the associated triangular ring. It is shown that every additive generalized Jordan (triple) higher derivation on $\mathcal{U}$ is a generalized higher derivation.