Pre-symmetric c-distances and characterization of complete cone metric spaces

The main goal of this research is to express the definition of pre-symmetric c-distances in cone metric spaces inspired by pre-symmetric w-distances defined by Romaguera and Tirado [Mathematics. 12 (2024), 2:305] and give the properties of this type of c-distances along with some examples. Then we introduce Suzuki's theorem regarding a pre-symmetric c-distance and obtainrelationship between several important contractions with respect to cone metric spaces. Finally, we will state a characterization of the completeness of cone metrics using fixed point theorems, which is different from previous descriptions of complete cone metric spaces.