Skip to main content
SpringerLink
Log in

Fixed point theorems for single- and set-valued F-contractions in b-metric spaces

  • Published:
Journal of Fixed Point Theory and Applications Aims and scope Submit manuscript

Abstract

Very recently, Miculescu and Mihail in (J. Fixed Point Theory Appl 19:2153–2163, 2017) gave a sufficient condition for Cauchyness on sequences in b-metric spaces. In this paper, we give a weaker sufficient condition. Also, to show the new sufficient condition is reasonably weak, we give an example. Using the new sufficient condition, we prove fixed point theorems for set-valued F-contractions in complete b-metric spaces. We also prove a fixed point theorem for single-valued F-contractions in complete b-metric spaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Altun, İ., Mınak, G., Dăg, H.: Multivalued \(F\)-contractions on complete metric spaces. J. Nonlinear Convex Anal. 16, 659–666 (2015). MR3343167

    MathSciNet  MATH  Google Scholar 

  2. Czerwik, S.: Nonlinear set-valued contraction mappings in \(b\)-metric spaces. Atti Sem. Mat. Fis. Univ. Modena 46, 263–276 (1998). MR1665883

    MathSciNet  MATH  Google Scholar 

  3. Heinonen, J.: Lectures on Analysis on Metric Spaces. Springer, Berlin (2001). MR1800917

    Book  MATH  Google Scholar 

  4. Jachymski, J.: Remarks on contractive conditions of integral type. Nonlinear Anal. 71, 1073–1081 (2009). MR2527526

    Article  MathSciNet  MATH  Google Scholar 

  5. Jachymski, J., Matkowski, J., Świa̧tkowski, T.: Nonlinear contractions on semimetric spaces. J. Appl. Anal 1, 125–134 (1995). MR1395268

    Article  MathSciNet  MATH  Google Scholar 

  6. Miculescu, R., Mihail, A.: New fixed point theorems for set-valued contractions in \(b\)-metric spaces. J. Fixed Point Theory Appl. 19, 2153–2163 (2017). MR3692446

    Article  MathSciNet  MATH  Google Scholar 

  7. Suzuki, T.: Discussion of several contractions by Jachymski’s approach. Fixed Point Theory Appl. 2016, 91 (2016). MR3548683

  8. Suzuki, T.: Basic inequality on a \(b\)-metric space and its applications, J. Inequal. Appl. 2017, 256 (2017). MR3711630

  9. Suzuki, T.: Fixed point theorems for contractions in semicomplete semimetric spaces (submitted)

  10. Suzuki, T., Kikkawa, M.: Generalizations of both Ćirić’s and Bogin’s fixed point theorems. J. Nonlinear Convex Anal. 17, 2183–2196 (2016). MR3597354

    MathSciNet  MATH  Google Scholar 

  11. Wardowski, D.: Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012, 94 (2012). MR2949666

Download references

Acknowledgements

The author is supported in part by JSPS KAKENHI Grant Number 16K05207 from Japan Society for the Promotion of Science.

Author information

Authors and Affiliations

  1. Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu, 804-8550, Japan

    Tomonari Suzuki

Authors
  1. Tomonari Suzuki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomonari Suzuki.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Suzuki, T. Fixed point theorems for single- and set-valued F-contractions in b-metric spaces. J. Fixed Point Theory Appl. 20, 35 (2018). https://doi.org/10.1007/s11784-018-0519-4

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s11784-018-0519-4

Keywords

Mathematics Subject Classification

Search

Navigation