About: Functional equation of Dhombres type - a simple equation with many open problems

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We consider continuous solutions f(x), x>0, of the functional equation f(xf(x))=H(f(x)), when H is a given continuous map without any restrictions. Concerning continuous solutions, the case when H is an increasing homeomorphism, is completely described, in the other cases there are only partial results. This paper contains a survey of known results, new results showing how the equation can be simplified in the general case, and some open problems and conjectures. In particular, can the range of a solution contain a periodic orbit of H of period different from 1 and 2? We provide auxillary results that could be of some use. Finally, this equation was also considered in the complex domain and some classes of entire and/or locally analytic solutions are described. Again, there are open problems here. We consider continuous solutions f(x), x>0, of the functional equation f(xf(x))=H(f(x)), when H is a given continuous map without any restrictions. Concerning continuous solutions, the case when H is an increasing homeomorphism, is completely described, in the other cases there are only partial results. This paper contains a survey of known results, new results showing how the equation can be simplified in the general case, and some open problems and conjectures. In particular, can the range of a solution contain a periodic orbit of H of period different from 1 and 2? We provide auxillary results that could be of some use. Finally, this equation was also considered in the complex domain and some classes of entire and/or locally analytic solutions are described. Again, there are open problems here. (en)
Title	Functional equation of Dhombres type - a simple equation with many open problems Functional equation of Dhombres type - a simple equation with many open problems (en)
skos:prefLabel	Functional equation of Dhombres type - a simple equation with many open problems Functional equation of Dhombres type - a simple equation with many open problems (en)
skos:notation	RIV/47813059:19610/09:#0000262!RIV10-MSM-19610___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika	11
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Smítal, Jaroslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	315711
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/09:#0000262
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	iterative functional equation; invariant curves; converse problem; real solutions; locally analytic solutions; entire solutions (en)
http://linked.open.../riv/klicoveSlovo	converse problem entire solutions locally analytic solutions invariant curves iterative functional equation real solutions
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[97872959B08B]
http://linked.open...i/riv/nazevZdroje	Journal of Difference Equations and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	15
http://linked.open...iv/tvurceVysledku	Smítal, Jaroslav Reich, Ludwig
http://linked.open...n/vavai/riv/zamer	Topological and analytical methods in the theory of dynamical systems and mathematical physics
issn	1023-6198
number of pages	13 (xsd:int)
http://localhost/t...ganizacniJednotka	19610
is http://linked.open...avai/riv/vysledek of	Functional equation of Dhombres type - a simple equation with many open problems Functional equation of Dhombres type - a simple equation with many open problems Functional equation of Dhombres type - a simple equation with many open problems Functional equation of Dhombres type - a simple equation with many open problems

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