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.
"IMPLICIT AND EXPLICIT ALGORITHMS FOR MINIMUM-NORM FIXED POINTS OF PSEUDOCONTRACTIONS IN HILBERT SPACES." Taiwanese J. Math. 16 (4) 1489 - 1506, 2012. https://doi.org/10.11650/twjm/1500406745