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Description
| - We consider the functional equation $f(xf(x))=\varphi (f(x))$ where $\varphi: J\rightarrow J$ is a given increasing homeomorphism of an open interval $J\subset (0,\infty )$, and $f:(0,\infty )\rightarrow J$ is an unknown continuous function. We proved that no continuous solution can cross the line $y=p$ where $p$ is a fixed point of $\varphi$, with a possible exception for $p=1$. The range of any non-constant continuous solution is an interval whose end-points are fixed by $\varphi$ and which containsin its interior no fixed point except for $1$. We also gave a characterization of the class of continuous monotone solutions and proved a condition sufficient for any continuous function to be monotone. In the present paper we give a characterization of the equations which have all continuous solutions monotone. All continuous solutions are monotone if either (i) 1 is an end-point of $J$ and $J$ contains no fixed point of $\varphi$, or (ii) $1\in J$ and $J$ contains no fixed points different from 1.
- We consider the functional equation $f(xf(x))=\varphi (f(x))$ where $\varphi: J\rightarrow J$ is a given increasing homeomorphism of an open interval $J\subset (0,\infty )$, and $f:(0,\infty )\rightarrow J$ is an unknown continuous function. We proved that no continuous solution can cross the line $y=p$ where $p$ is a fixed point of $\varphi$, with a possible exception for $p=1$. The range of any non-constant continuous solution is an interval whose end-points are fixed by $\varphi$ and which containsin its interior no fixed point except for $1$. We also gave a characterization of the class of continuous monotone solutions and proved a condition sufficient for any continuous function to be monotone. In the present paper we give a characterization of the equations which have all continuous solutions monotone. All continuous solutions are monotone if either (i) 1 is an end-point of $J$ and $J$ contains no fixed point of $\varphi$, or (ii) $1\in J$ and $J$ contains no fixed points different from 1. (en)
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Title
| - On generalized Dhombres functional equation
- On generalized Dhombres functional equation (en)
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skos:prefLabel
| - On generalized Dhombres functional equation
- On generalized Dhombres functional equation (en)
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skos:notation
| - RIV/47813059:19610/01:00000054!RIV/2002/GA0/196102/N
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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(GA201/97/0001), Z(MSM 192400002)
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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/47813059:19610/01:00000054
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - %22iterative functional equation; invariant curves; monotone solutions%22 (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - CH - Švýcarská konfederace
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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...ocetUcastnikuAkce
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http://linked.open...nichUcastnikuAkce
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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
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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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