The sufficient and necessary conditions of two single-valued mapping and a set-valued mapping with the only common fixed point in complete metric space are discussed.

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.

In this paper, we will give a new type of fixed point theorem for non - self - mapping in a complete metrically convex metric space.