Strong convergence theorems for split variational inequality problems in Hilbert spaces

In this paper, we consider the variational inequality problem and the split common fixed point problem. Considering the common fixed points of an infinite family of nonexpansive mappings, instead of just the fixed point of one nonexpansive mapping, we generalize the results of Tian and Jiang. By removing a projection operator, we improve the efficiency of our algorithm. Finally, we propose a very simple modification to the extragradient method, which gives our algorithm strong convergence properties. We also provide some numerical examples to illustrate our main results.