Let $\mathcal{A}$ be a unital ∗-algebra containing a nontrivial projection. In this paper, we show that every nonlinear mixed bi-skew Jordan-type higher derivation on $\mathcal{A}$ is an additive higher ∗-derivation. Moreover, we apply the above result to prime ∗-algebras, factor von Neumann algebras and standard operator algebras.

Let A be a unital prime *-algebra containing a nontrivial projection and ? be a nonzero scalar. We prove that a map ? : A ? A satisfies ?([A, B]? ?) = [?(A), B]? ? + [A,?(B)]? ? for all A, B ? A if and only if ? is an additive ?-derivation and ?(?A) = ??(A) for all A ? A, where [A, B]? ? = AB? ? ?BA?.

In this article, we give a sufficient and necessary condition for every Jordan {g,h}-derivation to be a {g,h}-derivation on triangular algebras. As an application, we prove that every Jordan {g,h}-derivation on $\tau (\mathcal{N})$ is a {g,h}-derivation if and only if $\dim 0_{+}\ne 1$ or $\dim H_{-}^{\perp }\ne 1$, where $\mathcal{N}$ is a non-trivial nest on a complex separable Hilbert space H and $\tau (\mathcal{N})$ is the associated nest algebra.