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In this paper we study iterative algorithms for finding a common element ofthe set of fixed points of $\kappa$-strict pseudocontractions or finding asolution of a variational inequality problem for a monotone, Lipschitzcontinuous mapping. The last problem being related to finding fixed points ofpseudocontractions. These algorithms were already studied in [G.L. Acedo, H.-K.Xu] and [N. Nadezhkina, W. Takahashi] but our aim here is to provide the linksbetween these know algorithms and the general framework of ${\cal T}$-classalgorithms studied in [H.H. Bauschke, P.L. Combettes].

${\cal T}$-class algorithms for pseudocontractions and $\kappa$-strict pseudocontractions in Hilbert spaces