The composition of two derivatives has a fixed point

Csörnyei, Marianna; O'Neil, Toby and Preiss, David (2001). The composition of two derivatives has a fixed point. Real Analysis Exchange, 26(2) pp. 749–760.

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Abstract

We show that if $f,g\colon [0,1]\to[0,1]$ are both Darboux Baire-1 functions, then their composition, $f\circ g$ possesses a fixed point.

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