The Study Of Some Partial-Order Methods

In this paper, we study the existence of fixed points in poset for multi-valued increasing operator which doesn't need compactness or continuity. We prove the existence of maximal and minimal fixed points for the multivalued increasing operator. For the operator equation , Lx = Nx,and inclusion equation, Lx∈Nx,we get the existence of the solutions in quasi-partial hoppy space using partial ordering method when the operators L and N are not continuous. Finally ,in lattice-ordered Banach space,the fixed points of a class of contractive mapping are discussed, and we get the uniqueness of fixed point for the contractive mapping.