The $Q^2$ dependence of polarized and unpolarized proton structure functions in the relativistic quark exchange framework

In this article we intend to discuss the evolution of polarized and unpolarized structure functions in the $(x,Q^2)$ plane. We analyze the proton data on the spin dependence asymmetry $A_1(x,Q^2)$, by making the dynamical assumption that at low resolution energies, the hadrons consist only of valence quarks and the scaling violation of $F_2(x,Q^2) $ at low $x$ comes only from the gluons density. While the sea quark and the gluon distributions are calculated using the inverse Mellin technique and the various moments of the valence quarks, the valence quark distribution itself is obtained from the relativistic quark-exchange model. A comparison is made with the corresponding available experimental data. Finally in agreement with the data, it is demonstrated that there is no significant $Q^2$-dependence of asymmetry $A_1(x, Q^2)$ for x ranging $0.014\le x \le 0.25$