This paper presents some existence and uniqueness theorems of the fixed point for ordered contractive mapping in Banach lattices. Moreover, we prove the existence of a unique solution for first-order ordinary differential equations with initial value conditions by using the theoretical results with no need for using the condition of a lower solution or an upper solution.
"Existence and Uniqueness Theorems of Ordered Contractive Map in Banach Lattices." Abstr. Appl. Anal. 2012 1 - 9, 2012. https://doi.org/10.1155/2012/191675