The main purpose of this article is to investigate the relation between different kinds of distances on divers metric spaces. Also, we consider some fixed point theorems with respect to a specified distance and show the validity of them regarding other distances. This helps researchers avoid constructing new theorems and additional proofs, which are indeed an illogical task. In particular, we discussed the fixed point theorems of Rahimi et al. with respect to w-distances (c-distances) and wt-distances (ct-distances).
