The Dynamic String-Averaging Algorithm for Inverse Strongly-Monotone Mappings with Nonsummable Errors

Abstract In the work by W. Takahashi and M. Toyoda (2003) it was established the weak convergence of an iteration process of solving a variational inequality problem. This variational inequality is associated with an inverse strongly-monotone mapping. In our recent research we showed that most of exact iterates of the same iterative process are approximate solutions of the variational inequality. In this paper we apply the dynamic string-averaging algorithm in order to find a common solution of a finite family of variational inequality problems, generated by inverse strongly-monotone mappings, and a finite family of fixed point problems for nonexpansive mappings under the presence of nonsummable computational errors. We show that the method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.