Geodesic
On fixed figure problems in fuzzy metric spaces
Kybernetika, Tome 59 (2023) no. 1, pp. 110-129.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Fixed circle problems belong to a realm of problems in metric fixed point theory. Specifically, it is a problem of finding self mappings which remain invariant at each point of the circle in the space. Recently this problem is well studied in various metric spaces. Our present work is in the domain of the extension of this line of research in the context of fuzzy metric spaces. For our purpose, we first define the notions of a fixed circle and of a fixed Cassini curve then determine suitable conditions which ensure the existence and uniqueness of a fixed circle (resp. a Cassini curve) for the self operators. Moreover, we present a result which prescribed that the fixed point set of fuzzy quasi-nonexpansive mapping is always closed. Our results are supported by examples.
DOI : 10.14736/kyb-2023-1-0110
Classification : 54A40, 54E35
Keywords: fixed circle; Archimedean $t$-norm; $M_h$-triangular fuzzy metric 
@article{10_14736_kyb_2023_1_0110,
     author = {Gopal, Dhananjay and Mart{\'\i}nez-Moreno, Juan and \"Ozg\"ur, Nihal},
     title = {On fixed figure problems in fuzzy metric spaces},
     journal = {Kybernetika},
     pages = {110--129},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {2023},
     doi = {10.14736/kyb-2023-1-0110},
     mrnumber = {4567844},
     zbl = {07675645},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2023-1-0110/}
}
TY  - JOUR
AU  - Gopal, Dhananjay
AU  - Martínez-Moreno, Juan
AU  - Özgür, Nihal
TI  - On fixed figure problems in fuzzy metric spaces
JO  - Kybernetika
PY  - 2023
SP  - 110
EP  - 129
VL  - 59
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2023-1-0110/
DO  - 10.14736/kyb-2023-1-0110
LA  - en
ID  - 10_14736_kyb_2023_1_0110
ER  - 
%0 Journal Article
%A Gopal, Dhananjay
%A Martínez-Moreno, Juan
%A Özgür, Nihal
%T On fixed figure problems in fuzzy metric spaces
%J Kybernetika
%D 2023
%P 110-129
%V 59
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2023-1-0110/
%R 10.14736/kyb-2023-1-0110
%G en
%F 10_14736_kyb_2023_1_0110
Gopal, Dhananjay; Martínez-Moreno, Juan; Özgür, Nihal. On fixed figure problems in fuzzy metric spaces. Kybernetika, Tome 59 (2023) no. 1, pp. 110-129. doi : 10.14736/kyb-2023-1-0110. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2023-1-0110/

Cité par Sources :