TY - JOUR
T1 - Eilenberg–Jachymski collections and its first consequences for the fixed point theory
AU - Berzig, Maher
AU - Kedim, Imed
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
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 - http://www.scopus.com/inward/record.url?scp=85103390596&partnerID=8YFLogxK
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 -