Applications of ball spaces theory: Fixed point theorems in semimetric spaces and ball convergence

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00567216" target="_blank" >RIV/67985840:_____/23:00567216 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11784-022-01030-y" target="_blank" >https://doi.org/10.1007/s11784-022-01030-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11784-022-01030-y" target="_blank" >10.1007/s11784-022-01030-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Applications of ball spaces theory: Fixed point theorems in semimetric spaces and ball convergence

Popis výsledku v původním jazyce

In the paper, we apply some of the results from the theory of ball spaces in semimetric setting. This allows us to obtain fixed point theorems which we believe to be unknown to this day. As a byproduct, we obtain the equivalence of some different notions of completeness in semimetric spaces where the distance function is 1-continuous. In the second part of the article, we generalize the Caristi-Kirk results for b-metric spaces. Additionally, we obtain a characterization of semicompleteness for 1-continuous b-metric spaces via a fixed point theorem analogous to a result of Suzuki. In the epilogue, we introduce the concept of convergence in ball spaces, based on the idea that balls should resemble closed sets in topological sets. We prove several of its properties, compare it with convergence in semimetric spaces and pose several open questions connected with this notion.

Název v anglickém jazyce

Applications of ball spaces theory: Fixed point theorems in semimetric spaces and ball convergence

Popis výsledku anglicky

In the paper, we apply some of the results from the theory of ball spaces in semimetric setting. This allows us to obtain fixed point theorems which we believe to be unknown to this day. As a byproduct, we obtain the equivalence of some different notions of completeness in semimetric spaces where the distance function is 1-continuous. In the second part of the article, we generalize the Caristi-Kirk results for b-metric spaces. Additionally, we obtain a characterization of semicompleteness for 1-continuous b-metric spaces via a fixed point theorem analogous to a result of Suzuki. In the epilogue, we introduce the concept of convergence in ball spaces, based on the idea that balls should resemble closed sets in topological sets. We prove several of its properties, compare it with convergence in semimetric spaces and pose several open questions connected with this notion.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-22230L" target="_blank" >GF20-22230L: Banachovy prostory spojitých a lipschitzovských funkcí</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Journal of Fixed Point Theory and Applications

ISSN

1661-7738

e-ISSN

1661-7746

Svazek periodika

25

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

26

Strana od-do

31

Kód UT WoS článku

000901234100002

EID výsledku v databázi Scopus

2-s2.0-85144292779