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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Common fixed points for compatible maps on the unit interval


Author: Gerald Jungck
Journal: Proc. Amer. Math. Soc. 115 (1992), 495-499
MSC: Primary 54H25
DOI: https://doi.org/10.1090/S0002-9939-1992-1105040-0
MathSciNet review: 1105040
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Abstract: Let $ g$ be a continuous self-map of the unit interval $ I$. It is proved that $ g$ has a common fixed point with every continuous function $ f:I \to I$ that is nontrivially compatible with $ g$ iff every periodic point of $ g$ is a fixed point of $ g$.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1105040-0
Article copyright: © Copyright 1992 American Mathematical Society

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