On generalized Dhombres functional equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F01%3A00000054" target="_blank" >RIV/47813059:19610/01:00000054 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On generalized Dhombres functional equation
Original language description
We consider the functional equation $f(xf(x))=varphi (f(x))$ where $varphi: Jrightarrow J$ is a given increasing homeomorphism of an open interval $Jsubset (0,infty )$, and $f:(0,infty )rightarrow J$ is an unknown continuous function. We proved that no continuous solution can cross the line $y=p$ where $p$ is a fixed point of $varphi$, with a possible exception for $p=1$. The range of any non-constant continuous solution is an interval whose end-points are fixed by $varphi$ and which containsinits interior no fixed point except for $1$. We also gave a characterization of the class of continuous monotone solutions and proved a condition sufficient for any continuous function to be monotone. In the present paper we give a characterization of the equations which have all continuous solutions monotone. All continuous solutions are monotone if either (i) 1 is an end-point of $J$ and $J$ contains no fixed point of $varphi$, or (ii) $1in J$ and $J$ contains no fixed points differe
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F97%2F0001" target="_blank" >GA201/97/0001: Dynamical systems</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2001
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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