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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F13%3A10173727%21RIV14-GA0-11320___
rdf:type
skos:Concept n18:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.1016/j.jmaa.2012.10.026
dcterms: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.
dcterms:title
Optimal approximate fixed point results in locally convex spaces Optimal approximate fixed point results in locally convex spaces
skos:prefLabel
Optimal approximate fixed point results in locally convex spaces Optimal approximate fixed point results in locally convex spaces
skos:notation
RIV/00216208:11320/13:10173727!RIV14-GA0-11320___
n18:predkladatel
n19:orjk%3A11320
n3:aktivita
n4:P
n3:aktivity
P(GAP201/12/0290)
n3:cisloPeriodika
1
n3:dodaniDat
n12:2014
n3:domaciTvurceVysledku
n10:8577048
n3:druhVysledku
n20:J
n3:duvernostUdaju
n8:S
n3:entitaPredkladatele
n11:predkladatel
n3:idSjednocenehoVysledku
94284
n3:idVysledku
RIV/00216208:11320/13:10173727
n3:jazykVysledku
n21:eng
n3:klicovaSlova
Uniformly continuous map; Sequentially continuous map; Totally bounded set; Approximate fixed point sequence; Approximate fixed point net
n3:klicoveSlovo
n16:Uniformly%20continuous%20map n16:Approximate%20fixed%20point%20net n16:Approximate%20fixed%20point%20sequence n16:Totally%20bounded%20set n16:Sequentially%20continuous%20map
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[C1F123FB070A]
n3:nazevZdroje
Journal of Mathematical Analysis and Applications
n3:obor
n7:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
3
n3:projekt
n9:GAP201%2F12%2F0290
n3:rokUplatneniVysledku
n12:2013
n3:svazekPeriodika
401
n3:tvurceVysledku
Kalenda, Ondřej Barroso, C. S. Reboucas, M. P.
n3:wos
000314739000001
s:issn
0022-247X
s:numberOfPages
8
n17:doi
10.1016/j.jmaa.2012.10.026
n13:organizacniJednotka
11320