Eilenberg–Jachymski collections and its first consequences for the fixed point theory

Maher Berzig; Imed Kedim

doi:10.1007/s11784-021-00854-4

Eilenberg–Jachymski collections and its first consequences for the fixed point theory

Maher Berzig
, Imed Kedim

Mathematics

University of Tunis

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we introduce the concept of Eilenberg–Jachymski collection on a nonempty set. Then, we establish three results equivalent to Bourbaki–Kneser’s fixed point theorem, and, therefore, to the axiom of choice. As consequences, we present new fixed point theorems in compact topological spaces, which extend and unify those of Nemytskii–Edelstein, Liepinš and Suzuki.

Original language	English
Article number	26
Journal	Journal of Fixed Point Theory and Applications
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/s11784-021-00854-4
State	Published - May 2021

Keywords

compact spaces
EJ-collections
fixed point theorems
partially ordered sets

Access to Document

10.1007/s11784-021-00854-4

Cite this

@article{c92711ce336440aa9cb074a1b11524d9,

title = "Eilenberg–Jachymski collections and its first consequences for the fixed point theory",

abstract = "In this paper, we introduce the concept of Eilenberg–Jachymski collection on a nonempty set. Then, we establish three results equivalent to Bourbaki–Kneser{\textquoteright}s fixed point theorem, and, therefore, to the axiom of choice. As consequences, we present new fixed point theorems in compact topological spaces, which extend and unify those of Nemytskii–Edelstein, Liepin{\v s} and Suzuki.",

keywords = "compact spaces, EJ-collections, fixed point theorems, partially ordered sets",

author = "Maher Berzig and Imed Kedim",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2021",

month = may,

doi = "10.1007/s11784-021-00854-4",

language = "English",

volume = "23",

journal = "Journal of Fixed Point Theory and Applications",

issn = "1661-7738",

publisher = "Springer Science + Business Media",

number = "2",

}

TY - JOUR

T1 - Eilenberg–Jachymski collections and its first consequences for the fixed point theory

AU - Berzig, Maher

AU - Kedim, Imed

PY - 2021/5

Y1 - 2021/5

N2 - In this paper, we introduce the concept of Eilenberg–Jachymski collection on a nonempty set. Then, we establish three results equivalent to Bourbaki–Kneser’s fixed point theorem, and, therefore, to the axiom of choice. As consequences, we present new fixed point theorems in compact topological spaces, which extend and unify those of Nemytskii–Edelstein, Liepinš and Suzuki.

AB - In this paper, we introduce the concept of Eilenberg–Jachymski collection on a nonempty set. Then, we establish three results equivalent to Bourbaki–Kneser’s fixed point theorem, and, therefore, to the axiom of choice. As consequences, we present new fixed point theorems in compact topological spaces, which extend and unify those of Nemytskii–Edelstein, Liepinš and Suzuki.

KW - compact spaces

KW - EJ-collections

KW - fixed point theorems

KW - partially ordered sets

UR - https://www.scopus.com/pages/publications/85103390596

U2 - 10.1007/s11784-021-00854-4

DO - 10.1007/s11784-021-00854-4

M3 - Article

AN - SCOPUS:85103390596

SN - 1661-7738

VL - 23

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 2

M1 - 26

ER -

Eilenberg–Jachymski collections and its first consequences for the fixed point theory

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this