LAUSR

In this paper, first, we introduce a new type of fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under gauge functions introduced by Fang in fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with property or property. Our results extend and improve very recent theorems in the related literature.