Solving of a Variational Inequality Problem Under the Presence of Computational Errors

W. Takahashi and M. Toyoda (2003) proved weak convergence of an iteration process of solving a variational inequality problem for an inverse strongly-monotone mapping. In our recent work we showed that, for the same iterative process, most of its exact iterates are approximate solutions of the variational inequality. In this paper, we show that the iteration process for solving a variational inequality problem for an inverse strongly monotone mapping generates an approximate solution in the presence of small computational errors. We also estimate a number of iterates needed in order to obtain such an approximate solution.