Abstract
Fixed circle problems belongs to a realm of problems in metric fixed
point theory. Specifically, it is a problem of finding self mappings
which remain invariant at each points 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.