The uniqueness of the best non-symmetric $$$L_1$$$-approximant with a weight by $$$A_{\alpha ,\beta }$$$-subspace

The questions of the uniqueness of the best non-symmetric $$$L_1$$$-approximant with weight in the finite dimensional subspace  and the connection of such tasks with  $$$A_{\alpha ,\beta }$$$-subspaces were considered in this article. This result generalizes the known result of Kroo on the case of non-symmetric approximation.