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.
Meiqiang Feng. Xuemei Zhang. Weigao Ge. "Positive Fixed Point of Strict Set Contraction Operators on Ordered Banach Spaces and Applications." Abstr. Appl. Anal. 2010 1 - 13, 2010. https://doi.org/10.1155/2010/439137