Abstract and Applied Analysis
Volume 2012 (2012), Article ID 926017, 15 pages
http://dx.doi.org/10.1155/2012/926017
Research Article

Minimum-Norm Fixed Point of Pseudocontractive Mappings

Habtu Zegeye,1 Naseer Shahzad,2 and Mohammad Ali Alghamdi2

1Department of Mathematics, University of Botswana, Private Bag 00704, Gaborone, Botswana
2Department of Mathematics, King Abdulaziz University, P.O. Box. 80203, Jeddah 21589, Saudi Arabia

Received 7 May 2012; Accepted 14 June 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Habtu Zegeye et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.