ON ITERATIONS OF DARBOUX FUNCTIONS

Tomasz Natkaniec

doi:10.2307/44152495

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Home > Journals > Real Anal. Exchange > Volume 20 > Issue 1 > Article

1994/1995 ON ITERATIONS OF DARBOUX FUNCTIONS

Tomasz Natkaniec

Real Anal. Exchange 20(1): 350-355 (1994/1995). DOI: 10.2307/44152495

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Abstract

If $f: \mathbb{R} \to \mathbb{R}$ is weakly connected and for every $x \in \mathbb{R}$ there is an $n_x$ with ${f^{{n_x}}}(x) = 1$ then $f(1) = 1$ . The analogous result holds for any Darboux function $f$ for which the set of all $n_x$ is bounded above.