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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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A fixed point theorem and attractors
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by Ludvik Janos and J. L. Solomon PDF
Proc. Amer. Math. Soc. 71 (1978), 257-262 Request permission

Abstract:

We investigate attractors for compact sets by considering a certain quotient space. The following theorem is included. Let $f:G \to G$, G a closed convex subset of a Banach space, f a mapping satisfying (i) there exists $M \subset G$ which is an attractor for compact sets under f; (ii) the family $\{ {f^n}\} _{n = 1}^\infty$ is equicontinuous. Then f has a fixed point.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 257-262
  • MSC: Primary 54H25
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0482716-2
  • MathSciNet review: 0482716