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

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Difference Equations and Applications

ISSN

1023-6198

e-ISSN

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Svazek periodika

15

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

13

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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