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