Covering mappings in metric spaces and fixed points

Covering mappings in metric spaces with fixed points was defined. Two assertions were made including contraction mapping principle and Milyutin's covering mapping theorem. The contraction mapping principle says that if a metric space is complete, any self-mapping of this space satisfying the Lipschitz condition with Lipschitz constant less than 1 has a fixed point. Milyutin's covering mapping theorem says that in case of a normed space and a continuous α-covering mapping where α<0, any mapping satisfying the Lipschitz condition with Lipschitz β <α, the mapping is (α-β) covering. The set valued mapping was said to be α-covering if it satisfies the Milyutin's covering mapping theorem.