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