Nonlinear bi-skew Jordan-type derivations on *-algebras

Abstract

Let $\mathcal {A}$ be a  unital $\ast$-algebra. In this paper, under some mild conditions on  $\mathcal {A}$, it is shown that $\delta$ is a nonlinear  bi-skew Jordan-type derivations on $\mathcal {A}$  if and only if $\delta$ is an additive $*-$derivation.  As applications, the nonlinear  bi-skew Jordan-type derivations on prime $\ast$-algebras, von Neumann algebras with no central summands of type $I_1$, factor von Neumann algebras and standard operator algebras are characterized.