Spojitá řešení zobecněné Dhombresovy funkcionální rovnice

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F04%3A00011716" target="_blank" >RIV/47813059:19610/04:00011716 - 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

The continuous solutions of a generalized Dhombres functional equation

Popis výsledku v původním jazyce

We consider the functional equation $f(xf(x))=varphi (f(x))$ where $varphi: Jrightarrow J$ is a given increasing homeomorphism of an open interval $Jsubset (0,infty )$ and $f:(0,infty )rightarrow J$ is an unknown continuous function. In a series of papers by P. Kahlig and J. Sm'{i}tal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under $varphi$ and which contains in its interior no fixed point except for $1$. They also provide a characterization of the class of monotone solutions and proved a necessary and sufficient condition for any solution to be monotone. In the present paper we give a characterization of the class of continuous solutions of this equation: We describe a method of constructing solutions as pointwise limits of solutions which are piecewise monotone on every compact subinterval. And we show that any solution can be obtained in this way. In particular, we show that if there exists a solution which is not m

Název v anglickém jazyce

The continuous solutions of a generalized Dhombres functional equation

Popis výsledku anglicky

We consider the functional equation $f(xf(x))=varphi (f(x))$ where $varphi: Jrightarrow J$ is a given increasing homeomorphism of an open interval $Jsubset (0,infty )$ and $f:(0,infty )rightarrow J$ is an unknown continuous function. In a series of papers by P. Kahlig and J. Sm'{i}tal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under $varphi$ and which contains in its interior no fixed point except for $1$. They also provide a characterization of the class of monotone solutions and proved a necessary and sufficient condition for any solution to be monotone. In the present paper we give a characterization of the class of continuous solutions of this equation: We describe a method of constructing solutions as pointwise limits of solutions which are piecewise monotone on every compact subinterval. And we show that any solution can be obtained in this way. In particular, we show that if there exists a solution which is not m

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

<a href="/cs/project/GP201%2F01%2FP134" target="_blank" >GP201/01/P134: Chaos v diskrétních dynamických systémech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2004

Kód důvěrnosti údajů

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

Název periodika

Mathematica Bohemica

ISSN

ISSN0862-7959

e-ISSN

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Svazek periodika

129

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

12

Strana od-do

399-410

Kód UT WoS článku

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EID výsledku v databázi Scopus

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