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

By Nihal Tas, Nihal Yilmaz Özgür, Nabil Mlaiki. Mathematics, 2018

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In this paper we investigate some fixed-circle theorems using Ćirić’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 Ćirić 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 Ćirić type F c -contraction to discontinuous self-mappings which have fixed circles.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cf31969d24465845a3ed3992c4f3e7c214f41ce5