فرنوش كيارستمي

In this thesis, we study the fixed-circle problem in metric spaces using generalized contractive conditions, including power-type contractions. First, by reviewing fundamental results from fixed-point an‎d fixed-circle theory, we establish the necessary foundation for developing new results. Subsequently, we examine several new types of contractions, such as Khan-FC an‎d Wardowski-FC contractions, which lead to novel fixed-circle theorems. Approaches related to common fixed circles are also presented, an‎d all theoretical results are analyzed through multiple illustrative examples. Finally, by employing power-type contractions an‎d modern auxiliary functions such as Ψ an‎d Ω , we present new results on the existence of fixed circles, demonstrating under what conditions all points on a given circle remain invariant under a self-mapping.

نقطه ثابت , دايره ثابت , مسئله دايره ثابت , دايره ثابت مشترك , ديسك ثابت , انقباض تواني , فضاهاي متريك

Fixed Point , Fixed Circle , Fixed-Circle Problem , Common Fixed Circle , Fixed Disc , Power-Type Contraction , Metric Spaces

Farnoosh Kiarostami

Dr. Asadollah Aghajani