Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 926209, 11 pages
doi:10.1155/2010/926209
Research Article

Fixed Points for Discontinuous Monotone Operators

Yujun Cui1 and Xingqiu Zhang2

1Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao 266510, China
2School of Mathematics, Liaocheng University, Liaocheng 252059, China

Received 24 September 2009; Accepted 21 November 2009

Academic Editor: Tomas Dominguez Benavides

Copyright © 2010 Yujun Cui and Xingqiu Zhang. 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 obtain some new existence theorems of the maximal and minimal fixed points for discontinuous monotone operator on an order interval in an ordered normed space. Moreover, the maximal and minimal fixed points can be achieved by monotone iterative method under some conditions. As an example of the application of our results, we show the existence of extremal solutions to a class of discontinuous initial value problems.