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A note on the relationship between the isotone assumption of the Abian-Brown fixed point theorem and Abian’s most basic fixed point theorem

Luckraz, Shravan

Authors

Shravan Luckraz Shravan.Luckraz@nottingham.edu.cn



Abstract

In a recent paper Xie et al. (Fixed Point Theory Appl. 2013:192, 2013) gave several extensions and some applications of the Abian-Brown (AB) fixed point theorem. While the AB fixed point theorem and its extensions (as well as other related fixed point theorems) assume that the mapping is isotone, this note shows that for single-valued finite maps this condition relates to the acyclicity of the map, which in turn relates to Abian’s (Nieuw Arch. Wiskd. XVI:184-185, 1968) most basic fixed point theorem for finite sets.

Citation

Luckraz, S. (2014). A note on the relationship between the isotone assumption of the Abian-Brown fixed point theorem and Abian’s most basic fixed point theorem. Fixed Point Theory and Applications, 2014(1), https://doi.org/10.1186/1687-1812-2014-129

Journal Article Type Article
Acceptance Date May 22, 2014
Publication Date May 29, 2014
Deposit Date Oct 17, 2017
Publicly Available Date Oct 17, 2017
Journal Fixed Point Theory and Applications
Electronic ISSN 1687-1812
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 2014
Issue 1
DOI https://doi.org/10.1186/1687-1812-2014-129
Keywords Isotone assumption; Fixed point theorem
Public URL http://eprints.nottingham.ac.uk/id/eprint/47162
Publisher URL https://doi.org/10.1186/1687-1812-2014-129
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0



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