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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)
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Title
| - Optimal approximate fixed point results in locally convex spaces
- Optimal approximate fixed point results in locally convex spaces (en)
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skos:prefLabel
| - Optimal approximate fixed point results in locally convex spaces
- Optimal approximate fixed point results in locally convex spaces (en)
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skos:notation
| - RIV/00216208:11320/13:10173727!RIV14-GA0-11320___
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/13:10173727
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Uniformly continuous map; Sequentially continuous map; Totally bounded set; Approximate fixed point sequence; Approximate fixed point net (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - US - Spojené státy americké
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Journal of Mathematical Analysis and Applications
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Kalenda, Ondřej
- Barroso, C. S.
- Reboucas, M. P.
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http://linked.open...ain/vavai/riv/wos
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issn
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number of pages
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http://bibframe.org/vocab/doi
| - 10.1016/j.jmaa.2012.10.026
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http://localhost/t...ganizacniJednotka
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