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The Omega Limit Sets of Ray-Contractive Operators

✍ Scribed by Yong-Zhuo Chen

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 83 KB
Volume: 261
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7541

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✦ Synopsis

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 -.

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