Department of Mathematics, Rzeszów University of Technology, P.O. Box 85, 35-595 Rzeszów, Poland
Academic Editor: William A. Kirk
Copyright © 2009 Jarosław Górnicki. 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.
The purpose of this paper is to prove, by asymptotic center techniques and the methods of Hilbert spaces, the following theorem. Let be a Hilbert space, let be a nonempty bounded closed convex subset of and let be a strongly ergodic matrix. If is a lipschitzian mapping such that , then the set of fixed points is a retract of . This result extends and improves the corresponding results of [7, Corollary 9] and [8, Corollary 1].