ABSTRACT
Fixed circle problems belong to a realm of problems in met- ric 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. In this chapter we introduce the concept of fixed circle in fuzzy metric spaces and 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 quasinonexpansive mapping is always closed. We conclude the chapter men- tioning some ideas for future research in this direction by putting forward some open questions.
