Weak and strong convergence theorems for solving pseudo-monotone variational inequalities with non-Lipschitz mappings

The aim of this paper is to study a classical pseudo-monotone and non-Lipschitz continuous variational inequality problem in real Hilbert spaces. Weak and strong convergence theorems are presented under mild conditions. Our methods generalize and extend some related results in the literature and the main advantages of proposed algorithms there is no use of Lipschitz condition of the variational inequality associated mapping. Numerical illustrations in finite and infinite dimensional spaces illustrate the behaviors of the proposed schemes.