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

DOI:
https://doi.org/10.1090/S0002-9939-08-09332-5

Published electronically:
September 29, 2008

MathSciNet review:
2448571

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Abstract | References | Similar Articles | 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:
https://doi.org/10.1090/S0002-9939-08-09332-5

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

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.