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

Abstract

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.

Keywords

• fixed circle
• Ćirić type Fc-contraction
• Hardy–Rogers type Fc-contraction
• Reich type Fc-contraction
• Chatterjea type Fc-contraction