Implicit and explicit algorithms for minimum-norm fixed points of pseudocontractions in Hilbert spaces

We introduce implicit and explicit iterative algorithms for the construction of fixed points of pseudocontractions T in Hilbert spaces. We prove that the proposed iterative algorithms converge strongly to the minimum-norm fixed point of T. Moreover we show that some of the existing iterative algorithms for nonexpansive mappings fail to converge when applied to pseudocontractions.