A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem

In this paper, we introduce and study a modified extragradient algorithm for approximating solutions of a certain class of split pseudo-monotone variational inequality problem in real Hilbert spaces. Using our proposed algorithm, we established a strong convergent result for approximating solutions of the aforementioned problem. Our strong convergent result is obtained without prior knowledge of the Lipschitz constant of the pseudo-monotone operator used in this paper, and with minimized number of projections per iteration compared to other results on split variational inequality problem in the literature. Furthermore, numerical examples are given to show the performance and advantage of our method as well as comparing it with related methods in the literature.