Abstract
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.
Citation
Márton Elekes. Tamás Keleti. Vilmos Prokaj. "The Composition of Derivatives Has a Fixed Point." Real Anal. Exchange 27 (1) 131 - 140, 2001/2002.
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