Comparison Between Ultrametric Space and Ultra-Suprametric Space

In this paper, our objective is to extend the concept of ultrametric spaces by presenting its corresponding structure, namely the ultra-suprametric spaces. of which we mention several properties related to balls. We try also to draw an analogy between ultra-suprametric spaces and ultrametric spaces. We conclude this section with a fixed point theorem of a new rational type contractive in complete ultra-suprametric spaces.