  We present a set of formula to extract exponents of the longitudinal
structure function and reduced cross section from the Regge-like behavior at
small $x$. The exponents are found to be independent of $Q^{2}$ at NNLO
analysis. As a result, we show that the reduced cross section exponents do not
have the same behavior at some values of $x$. This difference predicts the
non-linear effects and some evidence for shadowing and antishadowing at LHeC.
Also the ratio $\frac{F_{2}}{\sigma}$ is calculated and compared with the
corresponding HERA data. Our calculations show a very good agreement with the
DIS experimental data throughout the small values of $x$.
