The Dynamic String-Averaging Method for Inverse Strongly-Monotone Operators with Summable Errors

In the work by W. Takahashi and M. Toyoda (2003) it was introduced and studied an iterative process for solving a variational inequality problem which is induced by a inverse strongly-monotone mapping. They showed the weak convergence of the iteration process. Recently we established that most of exact iterates of the same iterative process are approximate solutions of the variational inequality. In the present work we use the dynamic string-averaging algorithm for finding 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. We study this algorithm in the presence of summable computational errors. It is shown that the cardinality of the set of iterates which are not approximate solutions is finite and does not exceed a certain constant which is calculated.