Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Fixed set theorems of Krasnoselskii type

Author: Efe A. Ok
Journal: Proc. Amer. Math. Soc. 137 (2009), 511-518
MSC (2000): Primary 47H04, 47H10; Secondary 47H09
Published electronically: September 29, 2008
MathSciNet review: 2448571
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Abstract: We revisit the fixed point problem for the sum of a compact operator and a continuous function, where the domain on which these maps are defined is not necessarily convex, the former map is allowed to be multi-valued, and the latter to be a semicontraction and/or a suitable nonexpansive map. In this setup, guaranteeing the existence of fixed points is impossible, but two types of invariant-like sets are found to exist.

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Additional Information

Efe A. Ok
Affiliation: Department of Economics, New York University, New York, New York 10012

Keywords: Fixed sets, Krasnoselski\u {\i } fixed point theorem, nonexpansive maps.
Received by editor(s): May 8, 2006
Received by editor(s) in revised form: April 16, 2007
Published electronically: September 29, 2008
Additional Notes: I thank Debraj Ray for his continuous support throughout my research on fixed set theory, and Cleon Barroso for pointing me to some related references. I should also acknowledge that the comments made by an anonymous referee have improved the exposition of this paper.
Communicated by: Marius Junge
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.