In this book we study the Krasnoselskii-Mann method in order to solve a common fixed point problem with a finite family of quasi-nonexpansive mappings acting of a convex set in a metric space with a hyperbolic structure. We consider several versions of the Krasnoselskii-Mann method associated with iterative algorithms, the Cimmino algorithm, methods with remotest set control, and dynamic string-averaging algorithms. Our goal is to study the convergence of iterates and obtain approximate solutions of the common fixed point problem under the presence of computational errors.