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Statements

Subject Item
n2:RIV%2F47813059%3A19610%2F05%3A%230000040%21RIV06-GA0-19610___
rdf:type
skos:Concept n19:Vysledek
dcterms: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. 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. 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.
dcterms:title
The converse problem for a generalized Dhombres functional equation Obrácený problém pro zobecněnou Dhombresovu funkcionální rovnici The converse problem for a generalized Dhombres functional equation
skos:prefLabel
Obrácený problém pro zobecněnou Dhombresovu funkcionální rovnici The converse problem for a generalized Dhombres functional equation The converse problem for a generalized Dhombres functional equation
skos:notation
RIV/47813059:19610/05:#0000040!RIV06-GA0-19610___
n3:strany
301;308
n3:aktivita
n9:Z n9:P
n3:aktivity
P(GA201/03/1153), Z(MSM4781305904)
n3:cisloPeriodika
3
n3:dodaniDat
n12:2006
n3:domaciTvurceVysledku
n13:7698143 n13:9159282
n3:druhVysledku
n15:J
n3:duvernostUdaju
n7:S
n3:entitaPredkladatele
n10:predkladatel
n3:idSjednocenehoVysledku
516405
n3:idVysledku
RIV/47813059:19610/05:#0000040
n3:jazykVysledku
n17:eng
n3:klicovaSlova
iterative functional equation; equation of invariant curves; general continuous solution; converse problem
n3:klicoveSlovo
n11:converse%20problem n11:equation%20of%20invariant%20curves n11:general%20continuous%20solution n11:iterative%20functional%20equation
n3:kodStatuVydavatele
CZ - Česká republika
n3:kontrolniKodProRIV
[49D45C036962]
n3:nazevZdroje
Mathematica Bohemica
n3:obor
n18:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
3
n3:projekt
n14:GA201%2F03%2F1153
n3:rokUplatneniVysledku
n12:2005
n3:svazekPeriodika
130
n3:tvurceVysledku
Reich, Ludwig Smítal, Jaroslav Štefánková, Marta
n3:zamer
n5:MSM4781305904
s:issn
0862-7959
s:numberOfPages
8
n16:organizacniJednotka
19610