A reformulation of the Gutzwiller-type approximation for so-called correlated ferrimagnetic states is developed to obtain an analytical expression for the ground-state energies. The physical properties of two-dimensional antiferromagnetic states in the doped regime, such as the longitudinal spin susceptibility and the charge compressibility, are calculated from this formalism. The authors have estimated the Landau parameters in Fermi liquid theory near the critical doping concentration for antiferromagnetism and the authors show the fundamental difference of these correlated antiferromagnetic systems with liquid ³He. In particular, the authors suggest the possibility of singlet superconductivity in the intermediate regime for the repulsive electron interaction (U approximately W) due to antiferromagnetic correlation.