Strong convergence result for solving monotone variational inequalities in Hilbert space

In this paper, we study strong convergence of the algorithm for solving classical variational inequalities problem with Lipschitz-continuous and monotone mapping in real Hilbert space. The algorithm is inspired by Tseng’s extragradient method and the viscosity method with a simple step size. A strong convergence theorem for our algorithm is proved without any requirement of additional projections and the knowledge of the Lipschitz constant of the mapping. Finally, we provide some numerical experiments to show the efficiency and advantage of the proposed algorithm.