In this dissertation we proved several results in quasi-pseudo metric spaces, fuzzy metric spaces, dislocated b-metric spaces and dislocated fuzzy metric spaces. These results are concerned with subspace instead of the whole space because in most of the situations the mappings are not contractive over the whole space. To overcome this problem we obtained necessary and sufficient conditions. Our results generalized the various results for L-fuzzy mappings and fuzzy mappings in left (right) K-sequentially complete quasi-pseudo metric spaces and complete dislocated b-metric spaces respectively. We also generalized the result of Banach for a family of multivalued mappings in fuzzy metric spaces and multivalued mappings in dislocated fuzzy metric spaces. Most of the fixed point results in this dissertation are proved for fuzzy mappings which is the generalization of multivalued mappings in fuzzy sets. Our analysis based upon the fact that the fuzzy fixed point results can be obtained from the fixed point theorem of multivalued mappings. These results are the generalization of various results in the existing literature. Several examples are also given in this dissertation to support our results.