Abstract and Applied Analysis
Volume 2010 (2010), Article ID 439137, 13 pages
doi:10.1155/2010/439137
Research Article

Positive Fixed Point of Strict Set Contraction Operators on Ordered Banach Spaces and Applications

Meiqiang Feng,1 Xuemei Zhang,2,3 and Weigao Ge3

1School of Applied Science, Beijing Information Science & Technology University, Beijing 100192, China
2Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
3Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 4 February 2010; Revised 8 May 2010; Accepted 7 July 2010

Academic Editor: Ferhan M. Atici

Copyright © 2010 Meiqiang Feng et al. 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

The fixed point theorem of cone expansion and compression of norm type for a strict set contraction operator is generalized by replacing the norms with a convex functional satisfying certain conditions. We then show how to apply our theorem to prove the existence of a positive solution to a second-order differential equation with integral boundary conditions in an ordered Banach space. An example is worked out to demonstrate the main results.