English

The Fixed Point of the Composition of Derivatives

Classical Analysis and ODEs 2011-09-27 v1

Abstract

We give an affirmative answer to a question of K. Ciesielski by showing that the composition fgf\circ g of two derivatives f,g:[0,1][0,1]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][0,1][0,1]\to[0,1] Darboux Baire-1 functions must also have a fixed point.

Keywords

Cite

@article{arxiv.1109.5303,
  title  = {The Fixed Point of the Composition of Derivatives},
  author = {Márton Elekes and Tamás Keleti and Vilmos Prokaj},
  journal= {arXiv preprint arXiv:1109.5303},
  year   = {2011}
}