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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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

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

  • 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