  In this paper, we study the strong convergence of two Mann-type inertial
extragradient algorithms, which are devised with a new step size, for solving a
variational inequality problem with a monotone and Lipschitz continuous
operator in real Hilbert spaces. Strong convergence theorems for our algorithms
are proved without the prior knowledge of the Lipschitz constant of the
operator. Finally, we provide some numerical experiments to illustrate the
performances of the proposed algorithms and provide a comparison with related
ones.
