Generalized Dhombres functional equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F17%3AA0000019" target="_blank" >RIV/47813059:19610/17:A0000019 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/chapter/10.1007/978-3-319-61732-9_13" target="_blank" >https://link.springer.com/chapter/10.1007/978-3-319-61732-9_13</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-61732-9_13" target="_blank" >10.1007/978-3-319-61732-9_13</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Generalized Dhombres functional equation

Popis výsledku v původním jazyce

We consider the equation f(xf(x)) = phi(f(x)), x &gt; 0, where phi is given, and f is an unknown continuous function (0,infinity)-&gt;(0,infinity). This equation was for the first time studied in 1975 by Dhombres (with phi(y) = y^2), later it was considered for other particular choices of phi, and since 2001 for arbitrary continuous function phi. The main problem, a classification of possible solutions and a description of the structure of periodic points contained in the range of the solutions (which appeared to be important way of the classification of solutions), was basically solved. This process involved not only methods from one-dimensional dynamics but also some new methods which could be useful in other problems. In this paper we provide a brief survey.

Název v anglickém jazyce

Generalized Dhombres functional equation

Popis výsledku anglicky

We consider the equation f(xf(x)) = phi(f(x)), x &gt; 0, where phi is given, and f is an unknown continuous function (0,infinity)-&gt;(0,infinity). This equation was for the first time studied in 1975 by Dhombres (with phi(y) = y^2), later it was considered for other particular choices of phi, and since 2001 for arbitrary continuous function phi. The main problem, a classification of possible solutions and a description of the structure of periodic points contained in the range of the solutions (which appeared to be important way of the classification of solutions), was basically solved. This process involved not only methods from one-dimensional dynamics but also some new methods which could be useful in other problems. In this paper we provide a brief survey.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název knihy nebo sborníku

Developments in Functional Equations and Related Topics

ISBN

9783319617312

Počet stran výsledku

7

Strana od-do

297-303

Počet stran knihy

352

Název nakladatele

Springer International Publishing

Místo vydání

Cham (Switzerland)

Kód UT WoS kapitoly

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