Divisible, reciprocal automorphisms of the unit interval
- Author
- Koen Maes and Bernard De Baets (UGent)
- Organization
- Abstract
- The Cauchy equation for automorphisms of the unit interval is fulfilled only by the identity mapping. We consider two weakened forms of this Cauchy equation: the reciprocity equation and the n-divisibility equation. Although the solution sets of both functional equations are quite large, requiring that an automorphism is both reciprocal and n-divisible, drastically increases the set of obligatory fixed points. However, increasing n also enlarges the domain on which the automorphism can be chosen freely. We also describe the solution sets of two functional equations that arise by composing the reciprocity and n-divisibility property.
- Keywords
- divisibility, Reciprocity, Cauchy equation, Cantor set, automorphism
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-692953
- MLA
- Maes, Koen, and Bernard De Baets. “Divisible, Reciprocal Automorphisms of the Unit Interval.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 17, no. 2, 2009, pp. 221–35, doi:10.1142/S0218488509005826.
- APA
- Maes, K., & De Baets, B. (2009). Divisible, reciprocal automorphisms of the unit interval. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 17(2), 221–235. https://doi.org/10.1142/S0218488509005826
- Chicago author-date
- Maes, Koen, and Bernard De Baets. 2009. “Divisible, Reciprocal Automorphisms of the Unit Interval.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 17 (2): 221–35. https://doi.org/10.1142/S0218488509005826.
- Chicago author-date (all authors)
- Maes, Koen, and Bernard De Baets. 2009. “Divisible, Reciprocal Automorphisms of the Unit Interval.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 17 (2): 221–235. doi:10.1142/S0218488509005826.
- Vancouver
- 1.Maes K, De Baets B. Divisible, reciprocal automorphisms of the unit interval. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS. 2009;17(2):221–35.
- IEEE
- [1]K. Maes and B. De Baets, “Divisible, reciprocal automorphisms of the unit interval,” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 17, no. 2, pp. 221–235, 2009.
@article{692953,
abstract = {{The Cauchy equation for automorphisms of the unit interval is fulfilled only by the identity mapping. We consider two weakened forms of this Cauchy equation: the reciprocity equation and the n-divisibility equation. Although the solution sets of both functional equations are quite large, requiring that an automorphism is both reciprocal and n-divisible, drastically increases the set of obligatory fixed points. However, increasing n also enlarges the domain on which the automorphism can be chosen freely. We also describe the solution sets of two functional equations that arise by composing the reciprocity and n-divisibility property.}},
author = {{Maes, Koen and De Baets, Bernard}},
issn = {{0218-4885}},
journal = {{INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS}},
keywords = {{divisibility,Reciprocity,Cauchy equation,Cantor set,automorphism}},
language = {{eng}},
number = {{2}},
pages = {{221--235}},
title = {{Divisible, reciprocal automorphisms of the unit interval}},
url = {{http://doi.org/10.1142/S0218488509005826}},
volume = {{17}},
year = {{2009}},
}
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