A unique Fixed Point Theorems in Fuzzy Metric Space with Applications

We study and extends some fuzzy metric space properties, the study provides some basic definitions and theorems in fuzzy metric space as well as the definition of equivalent of fuzzy metric spaces and their properties are discussed. Then we will continue to study compact sets in the fuzzy metric space as well as we have provided a definition of asymptotic sequences and proved some new results of them. A part of the main results of the fuzzy pseudo-metric space and its relationship to the fuzzy metric space, are also studied. In the last chapter has been put forward the concept of fixed point in fuzzy metric space complete and compact and concluded some of the results achieved there. In addition, we have discussed the study of two types of applications on the contraction function in the integration and Kannan function. Moreover, we have provided a new definition of the contraction function, we referred her to express ---contraction function and we proved some fixed point in orbitally f- complete in fuzzy metric space, Suzuki type fixed point and an ---contraction function.