Eilenberg–Jachymski collections and its first consequences for the fixed point theory

In this paper, we introduce the concept of Eilenberg–Jachymski collection on a nonempty set. Then, we establish three results equivalent to Bourbaki–Kneser’s fixed point theorem, and, therefore, to the axiom of choice. As consequences, we present new fixed point theorems in compact topological space...

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Bibliographic Details
Published in:Journal of fixed point theory and applications 2021-05, Vol.23 (2), Article 26
Main Authors: Berzig, Maher, Kedim, Imed
Format: Article
Language:English
Subjects:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Summary:In this paper, we introduce the concept of Eilenberg–Jachymski collection on a nonempty set. Then, we establish three results equivalent to Bourbaki–Kneser’s fixed point theorem, and, therefore, to the axiom of choice. As consequences, we present new fixed point theorems in compact topological spaces, which extend and unify those of Nemytskii–Edelstein, Liepinš and Suzuki.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-021-00854-4