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In this paper we investigate some fixed-circle theorems using Ciric’s technique (resp. Hardy-Rogers’ technique, Reich’s technique and Chatterjea’s technique) on a metric space. To do this, we define new types of F c -contractions such as Ciric type, Hardy-Rogers type, Reich type and Chatterjea type. Two illustrative examples are presented to show the effectiveness of our results. Also, it is given an application of a Ciric type F c -contraction to discontinuous self-mappings which have fixed circles.

New Types of Fc-Contractions and the Fixed-Circle Problem