Existence and Uniqueness Theorems of Ordered Contractive Map in Banach Lattices

الملخص EN

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.