This paper tries to define metric function for homeomorphic mapping, and a sufficient condition of bounded metric function is given, under which a upper bound of metric function is defined as well.

By the parametric representation, fuzzy number means a bounded continuous curve in the two-dimensional metric space R2, so that it is easy to analyze fuzzy differential equations.

Does research in a common fixed point theorem of fuzzy mappings in inequality conditions and the cut set is the nonempty closed bounded subsets of, while is complete metric space.