Fixed Point Theorem in Fuzzy Metric Space

In this present work, we prove fixed point theorem for contractive mapping F: X → X in fuzzy metric spaces that have a nonempty F− invariant complete subspace , then prove the uniqueness the fixed point in E.  Though many theorems in fuzzy metric space in this case, our theorem is a new type of these theorems as it is we proved that a unique fixed point there exists in F− invariant complete subset E in X. Finally, we give an interesting example in complete fuzzy metric space that satisfies in the conditions of our theorem and prove the uniqueness fixed point of F.