The Fixed Point of the Composition of Derivatives

Details The Fixed Point of the Composition of Derivatives The Fixed Point of the Composition of Derivatives

2011-09-24

arxiv.org/abs/1109.5303v1

Real Anal. Exchange 27 (2001/02), no. 1, 131-140

Mathematics

Classical Analysis and ODEs

Scientific paper

We give an affirmative answer to a question of K. Ciesielski by showing that
the composition $f\circ g$ of two derivatives $f,g:[0,1]\to[0,1]$ always has a
fixed point. Using Maximoff's Theorem we obtain that the composition of two
$[0,1]\to[0,1]$ Darboux Baire-1 functions must also have a fixed point.

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