  In this paper, we introduce an inertial proximal method for solving a bilevel
problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under
suitable conditions and without any restrictive assumption on the trajectories,
the weak and strong convergence of the sequence generated by the iterative
method are established. Two particular cases illustrating the proposed method
are thereafter discussed with respect to hierarchical minimization problems and
equilibrium problems under saddle point constraint. Furthermore, a numerical
example is given to demonstrate the implementability of our algorithm. The
algorithm and its convergence results improve and develop previous results in
the field.
