Non-linear mixed Jordan bi-skew Lie triple derivations on *-algebras

Abstract

In this article, we investigate the behaviour of a non-linear map $\Theta$ on $*$-algebra $\mathfrak{A}$, which satisfies $\Theta([X \circ Y, Z]_\bullet)=[\Theta(X)\circ Y, Z]_\bullet+[X\circ \Theta(Y), Z]_\bullet+ [X\circ Y, \Theta(Z)]_\bullet$, where $X \circ Y=XY + YX$ and $[X, Y]_\bullet=XY^*-YX^*$ (namely, Jordan and bi-skew Lie product, respectively), for all $X, Y, Z\in \mathfrak{A}$. Furthermore, we apply the above mentioned result to several distinct algebras.