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We show that, under appropriate conditions, one can create a hybrid between two given iterations which can perform better than either of the original ones. This fact provides a freedom of choice. We also give numerical examples in which we compare our hybrid with the dedicated Lee-Seung iteration.

We prove the equivalence between the -stabilities of the Krasnoselskij and the Mann iterations; a consequence is the equivalence with the -stability of the Picard-Banach iteration.