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We consider a Hubbard model with occupation dependent hopping integrals.Using the Hartree-Fock (H-F) approximation and the new Green function approachwith inter-site kinetic averages included, we analyze the influence of thecorrelated hopping on ferromagnetic ordering. The influence of correlatedhopping on the nonlocal quasiparticle energies and corresponding k-dependentspectral weights is included. In addition we obtain the shift of the spin bandswhich is a major factor in creating spontaneous ferromagnetism. At someparameters of the model the correlated hopping effect is strong enough toachieve saturated ferromagnetism. This state may be obtained at the asymmetricdensity of states (DOS) and the Fermi energy located in the region of largespectral weight near the band edge. The results are compared with DMFT-QuantumMonte Carlo calculations and with the Hubbard III approximation which includesthe correlated hopping effect.

New Green function approach describing the ferromagnetic state in the simple Hubbard model