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On two questions of A. Petruşel and G. Petruşel in b-metric fixed point theory

  • Nguyen Van Dung
  • Vo Thi Le Hang
Article

Abstract

In this paper, we study two questions of A. Petruşel and G. Petruşel in b-metric fixed point theory [12]. The main results of the paper are as follows.
  1. (1)

    Using the b-metric metrization theorem [9], fixed point results in the setting of b-metric spaces proved in [10, 11, 12] and some others may be seen as consequences of Ran–Reurings fixed point theorem in the classical metric spaces [13, Theorem 2.1]. This gives a partial answer to the question in [12, Remark 3.(2)].

     
  2. (2)

    Using the product space of two JS-metric spaces, main results of [12] and some others in the setting of b-metric spaces can be extended to the setting of JS-spaces. This answers the question in [12, Open question on page 1809].

     

Keywords

b-metric JS-metric fixed point metrization 

Mathematics Subject Classification

47H10 54H25 

Notes

Acknowledgements

The authors are greatly indebted to anonymous reviewers for their helpful comments to revise the paper.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Nonlinear Analysis Research GroupTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Journal of ScienceDong Thap UniversityCao Lanh CityVietnam
  4. 4.Faculty of Mathematics Teacher EducationDong Thap UniversityCao Lanh CityVietnam

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