Strong Convergence Theorems for Solving Variational Inequality Problems with Pseudo-monotone and Non-Lipschitz Operators

In this paper, we propose a new viscosity extragradient algorithm for solving variational inequality problems of pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. We prove a strong convergence theorem under some appropriate conditions imposed on the parameters. Finally, we give some numerical experiments to illustrate the advantages of our proposed algorithms. The main results obtained in this paper extend and improve some related works in the literature.