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Applications of Nonlinear Analysis pp 847–895Cite as

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

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 134))

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. 1.

    Introduction

  2. 2.

    Some Generalized Metric Spaces

  3. 3.

    New Generalizations of Rhoades’ Contractive Conditions

  4. 4.

    Some Generalizations of Nemytskii-Edelstein and Ćirić’s Fixed-Point Theorems

  5. 5.

    Some Fixed-Circle Theorems

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Authors and Affiliations

  1. Balıkesir University, Department of Mathematics, Balıkesir, Turkey

    Nihal Yılmaz Özgür & Nihal Taş

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  1. Nihal Yılmaz Özgür
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  2. Nihal Taş
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Correspondence to Nihal Yılmaz Özgür .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Özgür, N.Y., Taş, N. (2018). Generalizations of Metric Spaces: From the Fixed-Point Theory to the Fixed-Circle Theory. In: Rassias, T. (eds) Applications of Nonlinear Analysis . Springer Optimization and Its Applications, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-319-89815-5_28

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