Computational complexity of fixed points

A review of computational complexity results for approximating fixed points of Lipschitz functions is presented. Univariate and multivariate results are summarized for the second and infinity norm cases as well as the absolute, residual and relative error criteria. Contractive, nonexpansive, directionally nonexpansive, and expansive classes of functions are considered and optimal or nearly optimal algorithms exhibited. Some numerical experiments are summarized. A literature devoted to the complexity aspects of fixed point problems is listed.