Minimum-Norm Fixed Point of Pseudocontractive Mappings

Abstract EN

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 {yt}⊂K satisfying yt=βPK[(1−t)yt]+(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.