Several Fixed Point Theorems on Partially Ordered Banach Spaces and Applications

Abstract

In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by applying these theorems, we provide some existence and uniqueness of solutions to some integral equations. We also prove the solvability of some equilibrium problems in Banach spaces.