Generalized Dhombres functional equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F17%3AA0000019" target="_blank" >RIV/47813059:19610/17:A0000019 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/chapter/10.1007/978-3-319-61732-9_13" target="_blank" >https://link.springer.com/chapter/10.1007/978-3-319-61732-9_13</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-61732-9_13" target="_blank" >10.1007/978-3-319-61732-9_13</a>

Result language
angličtina
Original language name
Generalized Dhombres functional equation
Original language description
We consider the equation f(xf(x)) = phi(f(x)), x > 0, where phi is given, and f is an unknown continuous function (0,infinity)->(0,infinity). This equation was for the first time studied in 1975 by Dhombres (with phi(y) = y^2), later it was considered for other particular choices of phi, and since 2001 for arbitrary continuous function phi. The main problem, a classification of possible solutions and a description of the structure of periodic points contained in the range of the solutions (which appeared to be important way of the classification of solutions), was basically solved. This process involved not only methods from one-dimensional dynamics but also some new methods which could be useful in other problems. In this paper we provide a brief survey.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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