We obtain a result on the existence of a solution with big graph of functional equations of the form g(x,𝜑(x),𝜑(f(x)))=0 and we show that it is applicable to some important equations, both linear and nonlinear, including those of Abel, Böttcher and Schröder. The graph of such a solution 𝜑 has some strange properties: it is dense and connected, has full outer measure and is topologically big.
@article{bwmeta1.element.bwnjournal-article-cmv82i2p223bwm,
author = {Lech Bart\l omiejczyk},
title = {Solutions with big graph of iterative functional equations of the first order},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {223-230},
zbl = {0946.39006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv82i2p223bwm}
}
Bartłomiejczyk, Lech. Solutions with big graph of iterative functional equations of the first order. Colloquium Mathematicae, Tome 79 (1999) pp. 223-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i2p223bwm/
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