  In this article, we consider the ratio of structure functions for heavy quark
pair production at low values of $x$. The importance of this ratio for charm
and beauty pair production is examined according to the Hadron Electron Ring
Accelerator (HERA) data. The behavior of these ratios considers due to the
hard-pomeron behavior of the gluon distribution function. The results are in
good agreement with respect to the HERA data. Expanding this data to the range
of new energies underscore the importance of these measurements for heavy
quarks. The ratio of charm and beauty structure functions at the proposed Large
Hadron electron Collider (LHeC) is considered as a function of invariant
center-of-mass energy. For top pair production this ratio is extracted with
known kinematics of the LHeC and Future Circular Collider electron-hadron
(FCC-eh) colliders. Comparison of the results obtained for the ratio of top
structure functions in LHeC and FCC-eh are proportional to the specified
inelasticity $y$ range.
