as i know the exchange splitting cause Fe and some element and alloy become magnetize, now is there any relation between exchange interaction and exchange splitting.
I am not 100% sure I understand your question right, but I think the answer is: No.
If you look at the density of states for spin up and spin down in Fe, you will see that they are very similar, just offset by some energy. That offset is an estimate of the on-site exchange interaction, which is a result that is for itinerant magnets most commonly derived using Stoner theory. But: This parameter is not an inter-site exchange parameters that you would put into a Heisenberg(-like) Hamiltonian and there is no simple way of deriving such parameters from the basic Stoner exchange splitting of the bands. You can get an idea about the difficulties involved if you think about the information that you have from the band splitting - it just covers the z component of your magnetization (well, even just the size really). To describe the collective precession of spins in magnonic excitations you would need to somehow extract information about x and y components too.
The whole issue is really about the difference between single-particle excitations, described by the Stoner model and many-particle excitations, magnons, described by the Heisenberg model (there are also many-body excitations not described by the Heisenberg model, but we can usually neglect those). For an accessible account of these questions, I would recommend Peter Mohn's book Magnetism in the Solid State - An Introduction.
I recommend the text book by T. Moriya ¨Spin fluctuations¨, where shown in detail why the Stoner model is not sufficient and how to describe spin excitations in itinerant ferromagnets.
There is no relation between the exchange couplings (Fe-Fe for instance) and the splitting in the spin resolved DOS; In itinerant carriers mediated magnetism the exchange couplings have to be extracted from generalized susceptibility calculations in which the local exchange couplings enters,...it is the energy integral of a quantity of the form Fij(omega)=Tr(Gij,up(omega).Delta_i(omega)Gji,down(omega)Delta_j(omega)).f(omega)
where Gij,up, Gij,down are the greens between site i and j in up and down sector (they are usually matrices) Delta_i(omega) is the local exchange coupling at site i and f(omega) the Fermi distribution.
this kind of calculations have been performed within both first principle calculations or model studies, for systems such as alloys , diluted magnetic semiconductors, manganites,..