Abstract
K. Ciesielski asked whether the composition of two derivatives from the unit interval to itself always has a fixed point. The question is equivalent to asking if the composition of two Darboux, Baire one maps of $[0,1]$ to $[0,1]$ has a fixed point. The question is answered affirmatively for three subclasses of the Darboux, Baire one maps of $[0,1]$ to $[0,1]$
Citation
P. D. Humke. R. E. Svetic. C. E. Weil. "A Darboux Baire One Fixed Point Problem." Real Anal. Exchange 26 (2) 885 - 892, 2000/2001.
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