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A fixed point theorem and attractors

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Sep 1978 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 71, pages 257-262 (issn: 0002-9939, eissn: 1088-6826,

Authors: J. L. Solomon; Ludvik Janos;

doi: 10.1090/s0002-9939-1978-0482716-2 , 10.2307/2042845

A fixed point theorem and attractors

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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 → G f:G \to G , G a closed convex subset of a Banach space, f a mapping satisfying (i) there exists M ⊂ G M \subset G which is an attractor for compact sets under f; (ii) the family { f n } n = 1 ∞ \{ {f^n}\} _{n = 1}^\infty is equicontinuous. Then f has a fixed point.

Keywords

Fixed-point theorems

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