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Fixed set theorems of Krasnoselskii type
Author(s):
Efe
A.
Ok
Journal:
Proc. Amer. Math. Soc.
137
(2009),
511-518.
MSC (2000):
Primary 47H04, 47H10;
Secondary 47H09
Posted:
September 29, 2008
MathSciNet review:
2448571
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Additional information
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
Email:
efe.ok@nyu.edu
DOI:
10.1090/S0002-9939-08-09332-5
PII:
S 0002-9939(08)09332-5
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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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