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Generalizations of Metric Spaces: From the Fixed-Point Theory to the Fixed-Circle Theory

In: Applications of Nonlinear Analysis

Author

Listed:
  • Nihal Yılmaz Özgür

    (Department of Mathematics)

  • Nihal Taş

    (Department of Mathematics)

Abstract

This paper is a research survey about the fixed-point (resp. fixed-circle) theory on metric and some generalized metric spaces. We obtain new generalizations of the well-known Rhoades’ contractive conditions, Ćiri ć’s fixed-point result and Nemytskii-Edelstein fixed-point theorem using the theory of an S b-metric space. We present some fixed-circle theorems on an S b -metric space as a generalization of the known fixed-circle (fixed-point) results on a metric and an S-metric space. The content of this section is divided into the following: 1. Introduction 2. Some Generalized Metric Spaces 3. New Generalizations of Rhoades’ Contractive Conditions 4. Some Generalizations of Nemytskii-Edelstein and Ćirić’s Fixed-Point Theorems 5. Some Fixed-Circle Theorems

Suggested Citation

  • Nihal Yılmaz Özgür & Nihal Taş, 2018. "Generalizations of Metric Spaces: From the Fixed-Point Theory to the Fixed-Circle Theory," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Applications of Nonlinear Analysis, pages 847-895, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-89815-5_28
    DOI: 10.1007/978-3-319-89815-5_28
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