Solutions with big graph of iterative functional equations of higher orders
Lech Bartołomiejczyk, Janusz Morawiec (2005)
Acta Universitatis Carolinae. Mathematica et Physica
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Lech Bartołomiejczyk, Janusz Morawiec (2005)
Acta Universitatis Carolinae. Mathematica et Physica
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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.
Don R. Lick (1976)
Colloquium Mathematicae
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Dragoš M. Cvetković, Irena Pevac (1983)
Publications de l'Institut Mathématique
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D. M. Cvetković (1975)
Matematički Vesnik
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J. Nieminen (1975)
Applicationes Mathematicae
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