The deformations of antibracket with even and odd deformation parameters, defined on the space DE_1

We consider antiPoisson superalgebra realized on the smooth Grassmann-valued functions of the form xi f_0(x)+f_1(x), where f_0 has compact support on R, and with the parity opposite to that of the Grassmann superalgebra realized on these functions. The deformations with even and odd deformation parameters of this superalgebra are found.