Optimal approximate fixed point results in locally convex spaces

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimal approximate fixed point results in locally convex spaces

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Optimal approximate fixed point results in locally convex spaces

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topologické a geometrické vlastnosti Banachových prostorů a operátorových algeber</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

401

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

8

Strana od-do

1-8

Kód UT WoS článku

000314739000001

EID výsledku v databázi Scopus

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