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.
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.