By using a perturbative canonical transformation and mean field theory

the parameter regimes that give rise to ferromagnetism are determined in the one-dimensional Hubbad-Hirsch model. The model decribes a tight-binding band with on-site repulsion U. nearest-neighbor Coulomb exchange matrix element J" and doping parameter δ.Ferromagnetism only occurs for J">0. with the required value of J" decreasing as U increases and increasing as δ increases. The ferromagnetism regions are always smaller than that for half-filling for a fixed J".