Minimum-Norm Fixed Point of Pseudocontractive Mappings - Habtu Zegeye; Naseer Shahzad; Mohammad Ali Alghamdi (Abstract and Applied Analysis)
Let K be a closed convex subset of a real Hilbert space H and let be a continuous pseudocontractive mapping. Then for and each , there exists a sequence satisfying which converges strongly, as , 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.