In this article, we proved fixed point theorems using contraction mappings in the metric space. Specifically, we deal among the space of multiplicative metric in which we obtain fixed point using the self mappings. At the beginning of this paper, we discuss few essential definitions and lemmas that contribute to our main theorems. Our main theorem includes few fixed points results, which were derived by proving the existence together with the uniqueness of fixed point in the multiplicative metric space. Eventually, we obtain the results involving fixed points using double self mappings in the complete multiplicative metric space.