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

Jachymski, Jacek

doi:10.1090/S0002-9939-96-03397-7

Equivalent conditions involving common fixed points for maps on the unit interval
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by Jacek R. Jachymski PDF

Proc. Amer. Math. Soc. 124 (1996), 3229-3233 Request permission

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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