An Algorithm with Remote Set Control for Inverse Strongly Monotone Mappings

In 2003, W. Takahashi and M. Toyoda established the weak convergence of the 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 the exact iterates of the same iterative process are approximate solutions of the variational inequality. In this paper, we apply a method with remote set control in order to find a common solution of a family of variational inequality problems, generated by inverse strongly monotone mappings, and a family of fixed point problems, which are not necessarily finite, in the presence of computational errors. Our results are obtained under the presence of summable and nonsummable computational errors.