  We present a set of formulas to extract the ratio
$F_{L}(x,Q^{2})/F_{2}(x,Q^{2})$ and $R(x,Q^{2})$ from the proton structure
function parameterized in the next-to-next-to-leading order of the perturbative
theory at low $x$ values. The behavior of these ratios are considered with
respect to the power-law behavior of the proton structure function. The results
are compared with experimental data and the color dipole model bounds. These
ratios are in good agreement with the HERA data throughout the fixed value of
the invariant mass. The behavior of these ratios controlled by the nonlinear
corrections at low values of $Q^{2}$. These results and comparison with HERA
data demonstrate that the suggested method for the ratio of structure functions
can be applied in analyses of the LHeC and FCC-eh projects.
