Geodesic
A new generalization of metric spaces satisfying the $T_2$-separation axiom and some related fixed point results
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2023), pp. 58-70

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, without using neither the compactness nor the uniform convexity, some fixed point theorems are proved by using a binary relation in the setting of a new class of spaces called $T$-partial metric spaces. This class of spaces can be considered the first generalization of metric spaces such that the generated topology is a Hausdorff topology. Our theorems generalize and improve very recent fixed point results in the literature. Finally, we show the existence of a solution for a class of differential equations under new weak conditions.
Keywords: fixed point, $T$-partial metric space, uniform convexity, $T_2$ separation axiom, integral equation. 
@article{IVM_2023_5_a6,
     author = {Y. Touail},
     title = {A new generalization of metric spaces satisfying the $T_2$-separation axiom and some related fixed point results},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {58--70},
     publisher = {mathdoc},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_5_a6/}
}
TY  - JOUR
AU  - Y. Touail
TI  - A new generalization of metric spaces satisfying the $T_2$-separation axiom and some related fixed point results
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 58
EP  - 70
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_5_a6/
LA  - ru
ID  - IVM_2023_5_a6
ER  - 
%0 Journal Article
%A Y. Touail
%T A new generalization of metric spaces satisfying the $T_2$-separation axiom and some related fixed point results
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 58-70
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_5_a6/
%G ru
%F IVM_2023_5_a6
Y. Touail. A new generalization of metric spaces satisfying the $T_2$-separation axiom and some related fixed point results. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2023), pp. 58-70. http://geodesic.mathdoc.fr/item/IVM_2023_5_a6/