Affine super Yangians and deformed double current superalgebras

We extend to the super Yangian of the special linear Lie superalgebra ${\mathfrak{s}\mathfrak{l}}_{m\mathrm{\mid }n}$ and its affine version certain results related to Schur-Weyl duality. We do the same for the deformed double current superalgebra of ${\mathfrak{s}\mathfrak{l}}_{m\mathrm{\mid }n}$, which is introduced here for the first time.