Summary: Let be a nonempty, closed and convex subset of a real Banach space . Let be a strictly pseudocontractive map in the sense of Browder and Petryshyn. For a fixed , define a sequence by
where is a real sequence defined in satisfying the following conditions: (i) , (ii) . Then . If, in addition, is demicompact, then converges strongly to some fixed point of .