In this thesis, we extend the idea of fuzzy mappings to generalized spaces like quasi-pseudo-metric spaces and cone metric spaces. Some notions namely α-commuting, α-weakly compatible mapping, L-fuzzy mappings for L-fuzzy sets, βFL - admissible for a pair of L-fuzzy mappings are also established. On the basis of the above definitions some interesting coincidence points, common fixed points and fixed point results are obtained which not only generalize many important results of fuzzy mappings and multivalued mappings in the recent literature but also deduce a few existence theorems for the solution of generalized class of nonlinear integral equations. To enhance the validity of this work some practical examples are also furnished.