The existence of maximal and minimal fixed points for various set-valued operators is discussed. This paper presents some new fixed point theorems in ordered Banach spaces. A necessary and sufficient condition for the existence of the fixed point to a class of multivalued maps has been obtained. The uniqueness of the positive fixed point has been discussed. The results extend and improve the corresponding results. As an application, we utilize the results to study the existence and uniqueness of positive fixed points for a class of convex operators. In the end, we give a simple application to certain integral equations.