Abstract
We study the space of all continuous and increasing self-mappings of a real interval [a, b], where \(a<b\) are real numbers, equipped with the topology of uniform convergence. We show, in particular, that most such functions have infinitely many different fixed points.
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References
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Acknowledgements
The first author was partially supported by the Israel Science Foundation (Grant No. 820/17), by the Fund for the Promotion of Research at the Technion (Grant No. 2001893) and by the Technion General Research Fund (Grant No. 2016723). Both authors are grateful to an anonymous referee for many useful comments and helpful suggestions.
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Reich, S., Zaslavski, A.J. Most continuous and increasing functions on a compact real interval have infinitely many different fixed points. J. Fixed Point Theory Appl. 25, 53 (2023). https://doi.org/10.1007/s11784-023-01058-8
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DOI: https://doi.org/10.1007/s11784-023-01058-8