1Balikesir University, Department of Mathematics, 10145 Balikesir, Turkiye
Acta mathematica Universitatis Comenianae, Tome 92 (2023) no. 1, pp. 91-100
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Nihal Taş; Nihal Taş. Topological and geometric approach to the fixed-point theory with leakly rectified linear unit application. Acta mathematica Universitatis Comenianae, Tome 92 (2023) no. 1, pp. 91-100. http://geodesic.mathdoc.fr/item/AMUC_2023_92_1_a6/
@article{AMUC_2023_92_1_a6,
author = {Nihal Ta\c{s} and Nihal Ta\c{s}},
title = { Topological and geometric approach to the fixed-point theory with leakly rectified linear unit application},
journal = {Acta mathematica Universitatis Comenianae},
pages = {91--100},
year = {2023},
volume = {92},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2023_92_1_a6/}
}
TY - JOUR
AU - Nihal Taş
AU - Nihal Taş
TI - Topological and geometric approach to the fixed-point theory with leakly rectified linear unit application
JO - Acta mathematica Universitatis Comenianae
PY - 2023
SP - 91
EP - 100
VL - 92
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2023_92_1_a6/
ID - AMUC_2023_92_1_a6
ER -
%0 Journal Article
%A Nihal Taş
%A Nihal Taş
%T Topological and geometric approach to the fixed-point theory with leakly rectified linear unit application
%J Acta mathematica Universitatis Comenianae
%D 2023
%P 91-100
%V 92
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2023_92_1_a6/
%F AMUC_2023_92_1_a6
In this paper, we focus on the Banach contraction principle on $S_{b}$-metric spaces. At first, we give a brief history of the fixed-point theory and recall some necessary notions related to $S_{b}$-metric spaces. We present an alternative proof to the Banach contraction principle on $S_{b}$-metric spaces. Also, we investigate some geometric properties of the fixed-point set of a given self-mapping modifying the Banach contractive condition with an illustrative example. Finally, we obtain an application to Leakly rectified linear unit activation functions.
