AbstractLet (S1, d1), (S2, d2) be (closed subsets of) complete metric spaces, (S, d̃) = (S1× S2, d̃) and let T: S → S, × = Tx be a Lipschitz continuous operator (strictly) contractive in S for a suitable choice of its Lipschitz constants and of d̃. Conditions are given under which there may exist iteration procedures whose expense of computer time is lower than required by the usual iterative scheme xn=