Abstract and Applied Analysis
Volume 2011 (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

Ioan Gavrea and Mircea Ivan

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.