| In this paper, based on the theory of fuzzy metric space, severalproperties of fuzzy metric space are concerned.Firstly, some preliminaries important definitions and lemmas that are fre-quently used in the remaining chapters are provided. Secondly, this paper studiesthe completions and properties on L -fuzzy metric spaces based on the L -fuzzymetric introduced by R.Saadati who generalizes fuzzy metric. It especially provesBaire theorem on L -fuzzy metric spaces. Moreover, some fixed point theoremsfor fuzzy mappings on complete fuzzy metric space are performed. Finally, thistreatise generalizes the Hausdorff fuzzy metric in the sense of J.Rodriguez-Lopezand S.Romaguera, and introduce a new M_∞-fuzzy metric. It is also concernedwith some properties of M_∞-fuzzy metric. Furthermore, underφ-contraction con-dition, in the fuzzy metric space, several fixed point theorems on fuzzy sets arediscussed. |
