The extragradient method for finding a common solution of a finite family of variational inequalities and a finite family of fixed point problems in the presence of computational errors

In a Hilbert space, we study the convergence of the subgradient method to a common solution of a finite family of variational inequalities and of a finite family of fixed point problems under the presence of computational errors. Most results known in the literature establish the convergence of algorithms, when computational errors are summable. In the present paper, the convergence of the subgradient method is established for nonsummable computational errors. We show that the subgradient method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.