Real Analysis Exchange

The Composition of Two Derivatives Has a Fixed Point

Marianna Csörnyei, Toby C. O’Neil, and David Preiss

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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.

Article information

Real Anal. Exchange, Volume 26, Number 2 (2000), 749-760.

First available in Project Euclid: 27 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A99: None of the above, but in this section 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]

Darboux Baire-1 fixed points


Csörnyei, Marianna; O’Neil, Toby C.; Preiss, David. The Composition of Two Derivatives Has a Fixed Point. Real Anal. Exchange 26 (2000), no. 2, 749--760.

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