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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A fixed point theorem and attractors


Authors: Ludvik Janos and J. L. Solomon
Journal: Proc. Amer. Math. Soc. 71 (1978), 257-262
MSC: Primary 54H25
MathSciNet review: 0482716
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0482716-2
PII: S 0002-9939(1978)0482716-2
Keywords: Attractors for compact sets, equicontinuous family, quotient space, contractive mapping, retraction, fixed point
Article copyright: © Copyright 1978 American Mathematical Society