Abstract: By introducing two real function classes Σ and Γ on ［1,∞)³, the author gave the existence theorems of unique fixed points for mappings with σ(γ)-contractive conditions on multiplicative metric spaces, and gave Banach type fixed point theorem, Kannan type fixed point theorem, Chatterjea type fixed point theorem and Ciric type fixed point theorem and their generalized fixed point theorems on multiplicative metric spaces.

Key words: multiplicative metric space, fixed point, function class Σ, function class Γ