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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Equivalent conditions involving common fixed points for maps on the unit interval


Author: Jacek R. Jachymski
Journal: Proc. Amer. Math. Soc. 124 (1996), 3229-3233
MSC (1991): Primary 54H25; Secondary 54E45
MathSciNet review: 1328352
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Abstract: Let $g$ be a continuous self-map of the unit interval $I$. Equivalent conditions are given to ensure that $g$ has a common fixed point with every continuous map $f:I\mapsto I$ that commutes with $g$ on a suitable subset of $I$. This extends a recent result of Gerald Jungck.


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Additional Information

Jacek R. Jachymski
Affiliation: Institute of Mathematics, Technical University of Łódź, Żwirki 36, 90-924 Łódź, Poland
Email: jachymsk@lodz1.p.lodz.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03397-7
PII: S 0002-9939(96)03397-7
Keywords: Common fixed points, equicontinuity, commuting maps, iterates, unit interval
Received by editor(s): September 9, 1993
Received by editor(s) in revised form: March 29, 1995
Communicated by: James E. West
Article copyright: © Copyright 1996 American Mathematical Society