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.

中文翻译：

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新型模糊度量空间中广义Kannan型映射的不动点定理

在本文中，首先，我们介绍了一种新型的模糊度量空间，它是对模糊度量空间的推广。其次，研究模糊度量空间的拓扑性质。最后，在Fang引入的度量函数下，将Kannan型映射扩展到广义Kannan型映射，并证明了这种映射不动点的存在性和唯一性。此外，我们还获得了弱相容性的公共不动点定理，以及财产或财产。我们的结果扩展和改进了相关文献中的最新定理。