About: Optimal approximate fixed point results in locally convex 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)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1016/j.jmaa.2012.10.026
Description	Let C be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps f:C -> (C) over bar. First, we prove that, if f (C) is totally bounded, then it has an approximate fixed point net. Next, it is shown that, if C is bounded but not totally bounded, then there is a uniformly continuous map f:C -> C without approximate fixed point nets. We also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence. In contrast, it is observed that every affine (not-necessarily continuous) self-mapping of a bounded convex subset of a topological vector space has an approximate fixed point sequence. Moreover, we construct an affine sequentially continuous map from a compact convex set into itself without fixed points. Let C be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps f:C -> (C) over bar. First, we prove that, if f (C) is totally bounded, then it has an approximate fixed point net. Next, it is shown that, if C is bounded but not totally bounded, then there is a uniformly continuous map f:C -> C without approximate fixed point nets. We also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence. In contrast, it is observed that every affine (not-necessarily continuous) self-mapping of a bounded convex subset of a topological vector space has an approximate fixed point sequence. Moreover, we construct an affine sequentially continuous map from a compact convex set into itself without fixed points. (en)
Title	Optimal approximate fixed point results in locally convex spaces Optimal approximate fixed point results in locally convex spaces (en)
skos:prefLabel	Optimal approximate fixed point results in locally convex spaces Optimal approximate fixed point results in locally convex spaces (en)
skos:notation	RIV/00216208:11320/13:10173727!RIV14-GA0-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GAP201/12/0290)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2014
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	94284
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10173727
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Uniformly continuous map; Sequentially continuous map; Totally bounded set; Approximate fixed point sequence; Approximate fixed point net (en)
http://linked.open.../riv/klicoveSlovo	Approximate fixed point net Approximate fixed point sequence Sequentially continuous map Totally bounded set Uniformly continuous map
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[C1F123FB070A]
http://linked.open...i/riv/nazevZdroje	Journal of Mathematical Analysis and Applications
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 geometrical properties of Banach spaces and operator algebras
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	401
http://linked.open...iv/tvurceVysledku	Kalenda, Ondřej Barroso, C. S. Reboucas, M. P.
http://linked.open...ain/vavai/riv/wos	000314739000001
issn	0022-247X
number of pages	8 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.jmaa.2012.10.026
http://localhost/t...ganizacniJednotka	11320

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