## Fixed set theorems of Krasnoselskii type

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- Proc. Amer. Math. Soc.
**137**(2009), 511-518 Request permission

## 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.## References

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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
- 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
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2448571