The Cimmino Algorithm for Inverse Strongly-Monotone Mappings

In 2003 W. Takahashi and M. Toyodaestablished the weak convergence of an iteration process to solve a variational inequality problem induced by an inverse strongly-monotone mapping. Recently we proved that for the same iterative process, most of its exact iterates are approximate solutions of the variational inequality. It was also shown that the iteration process for solving a variational inequality problem for an inverse strongly-monotone mapping generates approximate solutions in the presence of computational errors. In this work we employ the Cimmino algorithm in order to generalize these results for common approximate solutions of a finite family of variational inequalities with inverse strongly-monotone mappings and of a finite family of fixed point problems in the presence of computational errors.