Fixed points of multiplicative contraction mappings on multiplicative   metric spaces
  In this paper, we first discussed multiplicative metric mapping by giving some topological properties of the relevant multiplicative metric space. As an interesting result of our discussions, we observed that the set of positive real numbers $\mathbb{R}_+$ is a complete multiplicative metric space with respect to the multiplicative absolute value function. Furthermore, we introduced concept of multiplicative contraction mapping and proved some fixed point theorems of such mappings on complete multiplicative metric spaces 
Muttalip Ozavsar and Adem Cengiz Cevikel
math.GM