Abstract and Applied Analysis
Volume 2011, Article ID 670509, 11 pages
http://dx.doi.org/10.1155/2011/670509
Research Article
Asymptotic Behaviour of the Iterates of Positive Linear Operators
Department of Mathematics, Technical University of Cluj-Napoca, Street Memorandumului 28, 400114 Cluj-Napoca, Romania
Received 4 December 2010; Accepted 20 March 2011
Academic Editor: Pavel Drábek
Copyright © 2011 Ioan Gavrea and Mircea Ivan. 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
We present a general result concerning the limit of the iterates of positive linear operators acting on continuous functions defined on a compact set. As applications, we deduce the asymptotic behaviour of the iterates of almost all classic and new positive linear operators.