Let K be a closed convex subset of a real Hilbert space H and let T : K → K be a continuous pseudocontractive mapping. Then for β ∈ 0, 1 and each t ∈ 0, 1 , there exists a sequence {y t } ⊂ K satisfying y t βP K 1 − t y t 1 − β T y t which converges strongly, as t → 0 , to the minimumnorm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.