Nonlinear bi-skew Jordan-type higher derivations on $\ast$-algebras

Abstract

This article studies the structure of nonlinear bi-skew Jordan-type higher derivations of unital $\ast$-algebras and proves that each nonlinear bi-skew Jordan-type higher derivation is an additive higher $\ast$-derivation. As applications, nonlinear bi-skew Jordan-type higher derivations on some classical unital $\ast$-algebras are characterized.