Nonlinear mixed $\ast$-Jordan type higher derivations on $\ast$-algebras

Abstract

In this paper, we show that any nonlinear mixed $\ast$-Jordan-type higher derivation on unital $\ast$-algebras is an additive higher $\ast$-derivation. As applications, nonlinear mixed $\ast$-Jordan-type higher derivations on some classical unital $\ast$-algebras, such as prime $\ast$-algebras, von Neumann algebras of type $I_1$, factor von Neumann algebras and standard operator algebras, are characterized, and some conclusions are extended.