Abstract: By introducing a real function class Φ on ［1,∞)⁴, we gave the existence theorems of unique common fixed point for two mappings satisfying the Φ-implicit condition on multiplicative metric spaces, and gave some (common) fixed point theorems. The conclusions generalized and improved the existing common fixed point theorems (in particular, the Banach-Chateajia type common fixed point theorems on multiplicative metric spaces). Finally, two examples were used to verify the correctness of the conclusions.

Key words: multiplicative metric space, function class Φ, implicit condition, common fixed point