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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fixed set theorems of Krasnoselskii type
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by Efe A. Ok PDF
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.
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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