  An approximately analysis study of the collinear approach for $t\overline{t}$
production at the Future Circular Collider hadron-electron (FCC-he) and the
Large Hadron electron Collider (LHeC) is performed. To study heavy quark
production processes, the collinear generalized double asymptotic scaling (DAS)
approach in a wide rang of $Q^{2}$ is used. The reduced cross sections for top
quark pair production at the FCC-he (for $Q^{2}{\geq}m^{2}_{t}$) and LHeC (for
$Q^{2}{\leq}m^{2}_{t}$) center-of-mass energies at the high inelasticity are
derived. These results may be considering for both the future collider
experiments at center-of-mass energy frontier and the improvement of the
phenomenological models on kinematics of low values of the Bjorken variable
$x$. The evolution of the gluon density for heavy-quark production in DIS is
obtained at low $x$ to include effects of heavy-quark masses. A nonlinear
modification of these results shown that the nonlinear corrections, with
respect to the top quark mass, are very small for $Q^{2}{\propto}m^{2}_{t}$.
