Functional equation of Dhombres type - a simple equation with many open problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F09%3A%230000262" target="_blank" >RIV/47813059:19610/09:#0000262 - 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
Functional equation of Dhombres type - a simple equation with many open problems
Original language description
We consider continuous solutions f(x), x>0, of the functional equation f(xf(x))=H(f(x)), when H is a given continuous map without any restrictions. Concerning continuous solutions, the case when H is an increasing homeomorphism, is completely described,in the other cases there are only partial results. This paper contains a survey of known results, new results showing how the equation can be simplified in the general case, and some open problems and conjectures. In particular, can the range of a solution contain a periodic orbit of H of period different from 1 and 2? We provide auxillary results that could be of some use. Finally, this equation was also considered in the complex domain and some classes of entire and/or locally analytic solutions are described. Again, there are open problems here.
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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Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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