New Types of F c -Contractions and the Fixed-Circle Problem

Nihal Taş, Nihal Yılmaz Özgür and Nabil Mlaiki
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Nihal Taş: Department of Mathematics, Balıkesir University, 10145 Balıkesir, Turkey
Nihal Yılmaz Özgür: Department of Mathematics, Balıkesir University, 10145 Balıkesir, Turkey
Nabil Mlaiki: Department of Mathematical Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Mathematics, 2018, vol. 6, issue 10, 1-9

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

Keywords: fixed circle; ?iri? type F c -contraction; Hardy–Rogers type F c -contraction; Reich type F c -contraction; Chatterjea type F c -contraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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