Kybernetika 59 no. 1, 110-129, 2023

On fixed figure problems in fuzzy metric spaces

Dhananjay Gopal, Juan Martínez-Moreno and Nihal ÖzgürDOI: 10.14736/kyb-2023-1-0110

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.

Keywords:

fixed circle, Archimedean $t$-norm, $M_h$-triangular fuzzy metric

Classification:

54A40, 54E35

paper.pdf

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