Optimal approximate fixed point results in locally convex spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10173727" target="_blank" >RIV/00216208:11320/13:10173727 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.10.026" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2012.10.026</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.10.026" target="_blank" >10.1016/j.jmaa.2012.10.026</a>
Alternative languages
Result language
angličtina
Original language name
Optimal approximate fixed point results in locally convex spaces
Original language 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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
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Volume of the periodical
401
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
8
Pages from-to
1-8
UT code for WoS article
000314739000001
EID of the result in the Scopus database
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