The Omega Limit Sets of Ray-Contractive Operators

In this paper, we study the omega limit sets of a ray-contractive map T without the compactness assumption on the orbits. If there exists a compact subset of ◦ K (the interior of a closed convex cone K) such that T = and T K − 0 ⊂ ◦ K , then we are able to prove that ω x either consists of a single point or forms a cycle 2 periodic orbit for any x ∈ ◦ K − .