We establish results on invariant approximation for fuzzy nonexpansive mappings defined on fuzzy metric spaces. As an application a result on the best approximation as a fixed point in a fuzzy normed space is obtained. We also define the strictly convex fuzzy normed space and obtain a necessary condition for the set of all $t$-best approximations to contain a fixed point of arbitrary mappings. A result regarding the existence of an invariant point for a pair of commuting mappings on a fuzzy metric...