Mathematica Moravica Vol. 27, No. 1 (2023), 73–83 New fixed-circle results on fuzzy metric spaces with an application to dynamic market equilibrium Elif Kaplan ∗ Abstract. In this study, the őxed point theory on fuzzy metric spaces has been generalized to the őxed-circle theory by making a geometric interpretation. The necessary conditions to exist the őxed circles of a self-mapping have been investigated and the uniqueness of the circle is examined under suitable conditions. We present some illustrative examples of obtained results and also ofer an application to conőrm the utility of our established result for őnding the unique solution of an integral equation appearing in the dynamic market equilibrium aspects of economics. 1. Introduction and Preliminaries The fuzzy set theory is one of the most valuable theories in solving uncertainty-related problems. Zadeh put forward this theory in 1965 [27]. Basic definitions and theorems of general topology have been generalized to fuzzy topological spaces. After that, one of this space’s primary problems is obtaining an appropriate notion of fuzzy metric spaces. Many authors studied this problem. Significantly, the authors in [1,3,8,11] have presented the concept of fuzzy metric space in various ways. George and Veeramani [4] have defined and studied a concept of fuzzy metric space with the help of continuous t-norm. The study of the relationship between fuzzy metric spaces and metric spaces constitutes a natural and interesting question in the theory of fuzzy metric spaces. In [4], it is proved that every metric space can induce a standard fuzzy metric spaces. Tas and Özgür [16] have recently pioneered a new trend by approaching the fixed point theory from a different perspective. Using the notion of a fixed circle, they and many researchers obtained valuable results on metric spaces and some generalized metric spaces [10, 12–15, 17–19, 22–25]. Also, Gopal et. al. [7] introduced the notion of a fixed circle in fuzzy metric spaces. 2020 Mathematics Subject Classification. Primary: 54E35; Secondary: 54E40. Key words and phrases. Fixed circle, Fuzzy metric, Dynamic market equilibrium. Full paper. Received 26 December 2022, accepted 22 March 2023, available online 22 March 2023. ©2023 Mathematica Moravica 73