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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Nihal Taş & Nihal Yılmaz Özgür & Nabil Mlaiki, 2018. "New Types of F c -Contractions and the Fixed-Circle Problem," Mathematics, MDPI, vol. 6(10), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:10:p:188-:d:173398
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