A projection Mann type iterative method, introduced in [K. Nakajo and W. Takahashi, J. Math. Anal. Appl. 279, No. 2, 372–379 (2003; Zbl 1035.47048)] and used there to approximate fixed points of nonexpansive mappings, is extended to a more general iterative method, appropriate for approximating fixed points of strict pseudocontractions. Let be a nonempty closed convex subset of a real Hilbert space and be a -strict pseudocontraction. In the present paper, the authors investigate the sequence generated by:
where is the metric projection. They show that converges weakly to a fixed point of (Theorem 3.1), or, respectively, converges strongly to (Theorem 4.1).