  We introduce regularity notions for averaged nonexpansive operators. Combined
with regularity notions of their fixed point sets, we obtain linear and strong
convergence results for quasicyclic, cyclic, and random iterations. New
convergence results on the Borwein-Tam method (BTM) and on the cylically
anchored Douglas-Rachford algorithm (CADRA) are also presented. Finally, we
provide a numerical comparison of BTM, CADRA and the classical method of cyclic
projections for solving convex feasibility problems.
