Fixed Points of Order Convex Maps in Ordered Banach Spaces

In this paper we discuss problems of the existence of fixed points of order convex maps. Lemma 1 Let (E,P) be an OBS,Suppose f: S_1→S_1 is a completely continuous map. Then f has fixed points in S_1. Lemma 2 Let (E,P) be an OBS whose positive cone is normal and has nonempty interior. Suppose f: P→P is a continuous, order increasing convex map, f(0)=0; such that. Then there exist a convex subset and a positive number r such that and.