Minimum‐Norm Fixed Point of Pseudocontractive Mappings
Habtu Zegeye, Naseer Shahzad, Mohammad Ali Alghamdi · Abstract and Applied Analysis · 2012
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.