On fixed figure problems in fuzzy metric spaces

Dhananjay Gopal; Juan Martínez-Moreno; Nihal Özgür

Kybernetika (2023)

  • Volume: 59, Issue: 1, page 110-129
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Gopal, Dhananjay, Martínez-Moreno, Juan, and Özgür, Nihal. "On fixed figure problems in fuzzy metric spaces." Kybernetika 59.1 (2023): 110-129. <http://eudml.org/doc/299070>.

@article{Gopal2023,
abstract = {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.},
author = {Gopal, Dhananjay, Martínez-Moreno, Juan, Özgür, Nihal},
journal = {Kybernetika},
keywords = {fixed circle; Archimedean $t$-norm; $M_h$-triangular fuzzy metric},
language = {eng},
number = {1},
pages = {110-129},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On fixed figure problems in fuzzy metric spaces},
url = {http://eudml.org/doc/299070},
volume = {59},
year = {2023},
}

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
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 1
SP - 110
EP - 129
AB - 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.
LA - eng
KW - fixed circle; Archimedean $t$-norm; $M_h$-triangular fuzzy metric
UR - http://eudml.org/doc/299070
ER -

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