About: On the approximate fixed point property in abstract spaces

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1007/s00209-011-0915-6
Description	Let X be a Hausdorff topological vector space, X * its topological dual and Z a subset of X . In this paper, we establish some results concerning the sigma(X,Z)-approximate fixed point property for bounded, closed convex subsets C of X. Three major situations are studied. First, when Z is separable in the strong topology. Second, when X is a metrizable locally convex space and Z = X , and third when X is not necessarily metrizable but admits a metrizable locally convex topology compatible with the duality. Our approach focuses on establishing the Frechet-Urysohn property for certain sets with regarding the sigma(X, Z)-topology. The support tools include the Brouwer's fixed point theorem and an analogous version of the classical Rosenthal's l_1-theorem for l_1-sequences in metrizable case. The results are novel and generalize previous work obtained by the authors in Banach spaces. Let X be a Hausdorff topological vector space, X * its topological dual and Z a subset of X . In this paper, we establish some results concerning the sigma(X,Z)-approximate fixed point property for bounded, closed convex subsets C of X. Three major situations are studied. First, when Z is separable in the strong topology. Second, when X is a metrizable locally convex space and Z = X , and third when X is not necessarily metrizable but admits a metrizable locally convex topology compatible with the duality. Our approach focuses on establishing the Frechet-Urysohn property for certain sets with regarding the sigma(X, Z)-topology. The support tools include the Brouwer's fixed point theorem and an analogous version of the classical Rosenthal's l_1-theorem for l_1-sequences in metrizable case. The results are novel and generalize previous work obtained by the authors in Banach spaces. (en)
Title	On the approximate fixed point property in abstract spaces On the approximate fixed point property in abstract spaces (en)
skos:prefLabel	On the approximate fixed point property in abstract spaces On the approximate fixed point property in abstract spaces (en)
skos:notation	RIV/00216208:11320/12:10127319!RIV13-AV0-11320___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100190901), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	3-4
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Kalenda, Ondřej
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	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	156353
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/12:10127319
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Frechet-Urysohn space; l_1 sequence; Metrizable locally convex space; Weak approximate fixed point property (en)
http://linked.open.../riv/klicoveSlovo	Weak approximate fixed point property Frechet-Urysohn space Metrizable locally convex space l_1 sequence
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[3A60EC954C37]
http://linked.open...i/riv/nazevZdroje	Mathematische Zeitschrift
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Topological and geometric structures in Banach spaces
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	271
http://linked.open...iv/tvurceVysledku	Kalenda, Ondřej Barroso, C. S. Lin, P-K
http://linked.open...ain/vavai/riv/wos	000306342700035
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	0025-5874
number of pages	15 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s00209-011-0915-6
http://localhost/t...ganizacniJednotka	11320

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