In this chapter we study the convergence of methods with remotest set control for solving common fixed point problems in a W-hyperbolic space using Krasnoselskii-Mann iterations. Our main goal is to obtain an approximate solution of the problem in the presence of computational errors. We show that the iterative method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant. Moreover, for a known computational error, we find out what an approximate solution can be obtained and how many iterates one needs for this.