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Displaying similar documents to “Solutions with big graph of iterative functional equations of the second order.”

Solutions with big graph of iterative functional equations of the first order

Lech Bartłomiejczyk (1999)

Colloquium Mathematicae

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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.