  We consider a Hubbard model with occupation dependent hopping integrals.
Using the Hartree-Fock (H-F) approximation and the new Green function approach
with inter-site kinetic averages included, we analyze the influence of the
correlated hopping on ferromagnetic ordering. The influence of correlated
hopping on the nonlocal quasiparticle energies and corresponding k-dependent
spectral weights is included. In addition we obtain the shift of the spin bands
which is a major factor in creating spontaneous ferromagnetism. At some
parameters of the model the correlated hopping effect is strong enough to
achieve saturated ferromagnetism. This state may be obtained at the asymmetric
density of states (DOS) and the Fermi energy located in the region of large
spectral weight near the band edge. The results are compared with DMFT-Quantum
Monte Carlo calculations and with the Hubbard III approximation which includes
the correlated hopping effect.
