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


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


Published: 2001/2002
First available in Project Euclid: 6 June 2008

zbMATH: 1011.26006
MathSciNet: MR1887687

Primary: 26A15 , 26A99 , 26B99 , 54H25

Keywords: composition , connected , derivative , fixed point , gradient , Level set

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 1 • 2001/2002
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