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

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Department of Mathematics, Balıkesir University, 10145 Balıkesir, Turkey
2
Department of Mathematical Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
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Author to whom correspondence should be addressed.
Mathematics 2018, 6(10), 188; https://doi.org/10.3390/math6100188
Received: 2 September 2018 / Revised: 26 September 2018 / Accepted: 27 September 2018 / Published: 2 October 2018
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. View Full-Text
Keywords: fixed circle; Ćirić type Fc-contraction; Hardy–Rogers type Fc-contraction; Reich type Fc-contraction; Chatterjea type Fc-contraction fixed circle; Ćirić type Fc-contraction; Hardy–Rogers type Fc-contraction; Reich type Fc-contraction; Chatterjea type Fc-contraction
MDPI and ACS Style

Taş, N.; Özgür, N.Y.; Mlaiki, N. New Types of Fc-Contractions and the Fixed-Circle Problem. Mathematics 2018, 6, 188. https://doi.org/10.3390/math6100188

AMA Style

Taş N, Özgür NY, Mlaiki N. New Types of Fc-Contractions and the Fixed-Circle Problem. Mathematics. 2018; 6(10):188. https://doi.org/10.3390/math6100188

Chicago/Turabian Style

Taş, Nihal, Nihal Y. Özgür, and Nabil Mlaiki. 2018. "New Types of Fc-Contractions and the Fixed-Circle Problem" Mathematics 6, no. 10: 188. https://doi.org/10.3390/math6100188

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