Investigation of the fixed-point theorem on a complete cone metric space

\nMetric space is the one of topics in mathematical analysis which is still being studied and developed. Previous research has extended the contraction mappings and completeness properties from metric spaces to other spaces such as cone metric spaces. This research will prove a fixed-point theorem on cone metric spaces, construct a function and maps to [0,1), then add several conditions to the theorem, namely partially ordered, contraction mapping, and non-decreasing and continuous functions. The outcomes include evidence indicating a unique fixed point in cone metric space. As consequence, there are three different characteristics for contraction mapping expressed in three corollaries.\n