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Description
| - We consider the functional equation $f(xf(x))=\varphi(f(x))$ where $\varphi J\rightarrow J$ is a given homeomorphism of an open interval $J\subset(0,\infty)$ and $f (0,\infty) \rightarrow J$ is an unknown continuous function. A characterization of the class $\Cal S(J,\varphi)$ of continuous solutions $f$ is given in a series of papers by Kahlig and Smital 1998-2002, and in a recent paper by Reich et al. 2004, in the case when $\varphi$ is increasing. In the present paper we solve the converse problem, for which continuous maps $f(0,\infty)\rightarrow J$, where $J$ is an interval, there is an increasing homeomorphism $\varphi$ of $J$ such that $f\in\Cal S(J,\varphi)$. We also show why the similar problem for decreasing $\varphi$ is difficult.
- We consider the functional equation $f(xf(x))=\varphi(f(x))$ where $\varphi J\rightarrow J$ is a given homeomorphism of an open interval $J\subset(0,\infty)$ and $f (0,\infty) \rightarrow J$ is an unknown continuous function. A characterization of the class $\Cal S(J,\varphi)$ of continuous solutions $f$ is given in a series of papers by Kahlig and Smital 1998-2002, and in a recent paper by Reich et al. 2004, in the case when $\varphi$ is increasing. In the present paper we solve the converse problem, for which continuous maps $f(0,\infty)\rightarrow J$, where $J$ is an interval, there is an increasing homeomorphism $\varphi$ of $J$ such that $f\in\Cal S(J,\varphi)$. We also show why the similar problem for decreasing $\varphi$ is difficult. (en)
- Uvažujeme funkcionální rovnici $f(xf(x))=\varphi(f(x))$ kde $\varphi J\rightarrow J$ je daný homeomorfizmus otevřeného intervalu $J\subset(0,\infty)$ a $f (0,\infty) \rightarrow J$ je neznámá funkce. Charakterizac třídy $\Cal S(J,\varphi)$ spojitých řešení $f$ jlze najít v sérii prací Kahliga a Smítala 1988 - 2002 a v nedávné práci Reich et al. 2004 v případě, kdy $\varphi$ je rostoucí. V této práci řešíme obrácený problém, která spojitá zobrazení $f (0,\infty)\rightarrow J$, kde $J$ je daný interval, existuje rostoucí homeomorfizmus $\varphi$ z $J$ na $J$ tak, že $f\in\Cal S(J,\varphi)$. Ukazujeme též, proč podobný problém s klesající funkcí $\varphi$ je obtížný. (cs)
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Title
| - The converse problem for a generalized Dhombres functional equation
- The converse problem for a generalized Dhombres functional equation (en)
- Obrácený problém pro zobecněnou Dhombresovu funkcionální rovnici (cs)
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skos:prefLabel
| - The converse problem for a generalized Dhombres functional equation
- The converse problem for a generalized Dhombres functional equation (en)
- Obrácený problém pro zobecněnou Dhombresovu funkcionální rovnici (cs)
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skos:notation
| - RIV/47813059:19610/05:#0000040!RIV06-GA0-19610___
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA201/03/1153), Z(MSM4781305904)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/47813059:19610/05:#0000040
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - iterative functional equation; equation of invariant curves; general continuous solution; converse problem (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Smítal, Jaroslav
- Štefánková, Marta
- Reich, Ludwig
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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