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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Name of the periodical

Journal of Fixed Point Theory and Applications

ISSN

1661-7738

e-ISSN

1661-7746

Volume of the periodical

25

Issue of the periodical within the volume

1

Country of publishing house

CH - SWITZERLAND

Number of pages

26

Pages from-to

31

UT code for WoS article

000901234100002

EID of the result in the Scopus database

2-s2.0-85144292779