Some Results on Partial Cone Metric Spaces with an Application

Abstract

 The objective of this paper is to determine some fixed point theorems for generalized  contractive mappings in the framework of partial cone metric spaces. In addition, we prove a unique fixed point theorem using a rational contractive condition. Our findings align with previous research in this area. We also show that our result can be applied to the problem of determining the existence of solutions to second-order differential equations.