New types of f-c-contractions and the fixed-circle problem

Abstract

In this paper we investigate some fixed-circle theorems using C ' iric ' ' 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 Fc-contractions such as C ' iric ' 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 C ' iric ' type Fc-contraction to discontinuous self-mappings which have fixed circles.