Minimum-norm fixed point of pseudocontractive mappings

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 βε(0,1) and each tε(0,1), there exists a sequence { y_t}⊂K satisfying yt=βPK[(1-t)y_t]+(1-β)T(yt) which converges strongly, as t→0⁺, to the minimum-norm 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.