Skip to main content
SpringerLink
Log in

Nonlinear contraction in b-suprametric spaces

  • Original Research Paper
  • Published:
The Journal of Analysis Aims and scope Submit manuscript

Abstract

We introduce the concept of b-suprametric spaces and establish a fixed point result for mappings satisfying a nonlinear contraction in such spaces. The obtained result generalizes a fixed point theorem of Czerwik and a recent result of the author.

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

Data availibility

Not applicable.

References

  1. Fagin, R., and L. Stockmeyer. 1998. Relaxing the triangle inequality in pattern matching. International Journal of Computer Vision 30: 219–231.

    Article  Google Scholar 

  2. Gragera, A., and V. Suppakitpaisarn. 2018. Relaxed triangle inequality ratio of the Sørensen-Dice and Tversky indexes. Theoretical Computer Science 718: 37–45.

    Article  MathSciNet  Google Scholar 

  3. Matthews, S.G. 1992. Partial metric spaces. Research Report 212, Dep. of Computer Science, University of Warwick RR 212, 1–19.

  4. Czerwik, S. 1993. Contraction mappings in \(b\)-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis 1 (1): 5–11.

    MathSciNet  Google Scholar 

  5. Branciari, A. 2000. A fixed point theorem of Banach–Caccioppoli type on a class of generalized metric spaces. Publicationes Mathematicae Debrecen 57 (1–2): 31–37.

    Article  MathSciNet  Google Scholar 

  6. Bugajewski, D., P. Maćkowiak, and R. Wang. 2020. On compactness and fixed point theorems in partial metric spaces. Fixed Point Theory 23 (1): 163–178.

    Article  MathSciNet  Google Scholar 

  7. Gregori, V., J.-J. Miñana, and D. Miravet. 2019. Fuzzy partial metric spaces. International Journal of General Systems 48 (3): 260–279.

    Article  MathSciNet  Google Scholar 

  8. Hoc, N.H., and L.V. Nguyen. 2022. Existence of minima of functions in partial metric spaces and applications to fixed point theory. Acta Mathematica Hungarica 168 (2): 345–362.

    Article  MathSciNet  Google Scholar 

  9. Kumar, S., and S. Luambano. 2021. On some fixed point theorems for multivalued \(f\)-contractions in partial metric spaces. Demonstratio Mathematica 54 (1): 151–161.

    Article  MathSciNet  Google Scholar 

  10. Afshari, H., and E. Karapınar. 2020. A discussion on the existence of positive solutions of the boundary value problems via \(\psi \)-Hilfer fractional derivative on \(b\)-metric spaces. Advances in Difference Equations 2020 (1): 1–11.

    MathSciNet  Google Scholar 

  11. Berzig, M., I. Kédim, and A. Mannai. 2018. Multivalued fixed point theorem in \(b\)-metric spaces and its application to differential inclusions. Filomat 32 (8): 2963–2976.

    Article  MathSciNet  Google Scholar 

  12. Boriceanu, M., M. Bota, and A. Petruşel. 2010. Multivalued fractals in \(b\)-metric spaces. Central European Journal of Mathematics 8: 367–377.

    Article  MathSciNet  Google Scholar 

  13. Lazreg, J.E., S. Abbas, M. Benchohra, and E. Karapınar. 2021. Impulsive Caputo-Fabrizio fractional differential equations in \(b\)-metric spaces. Open Mathematics 19 (1): 363–372.

    Article  MathSciNet  Google Scholar 

  14. Baradol, P., D. Gopal, and S. Radenović. 2020. Computational fixed points in graphical rectangular metric spaces with application. Journal of Computational and Applied Mathematics 375: 112805.

    Article  MathSciNet  Google Scholar 

  15. Budhia, L., H. Aydi, A.H. Ansari, and D. Gopal. 2020. Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations. Nonlinear Analysis: Modelling and Control 25 (4): 580–597.

    MathSciNet  Google Scholar 

  16. Turinici, M. 2021. Ekeland variational principles in \(2\)-local Branciari metric spaces. In Nonlinear Analysis and Global Optimization, 461–486. Berlin: Springer.

    Chapter  Google Scholar 

  17. Patil, J., B. Hardan, A.A. Hamoud, A. Bachhav, and H. Emadifar. 2022. A new result on Branciari metric space using \((\alpha, \gamma )\)-contractive mappings. Topological Algebra and its Applications 10 (1): 103–112.

    Article  MathSciNet  Google Scholar 

  18. Shukla, S. 2014. Partial rectangular metric spaces and fixed point theorems. The Scientific World Journal 756298: 1–7.

    Google Scholar 

  19. Roshan, J.R.R., V. Parvaneh, and Z. Kadelburg. 2016. New fixed point results in b-rectangular metric spaces. Nonlinear Analysis: Modelling and Control 21 (5): 614–634.

    Article  MathSciNet  Google Scholar 

  20. Abdeljawad, T., E. Karapınar, S.K. Panda, and N. Mlaiki. 2020. Solutions of boundary value problems on extended-Branciari \(b\)-distance. Journal of Inequalities and Applications 2020 (1): 1–16.

    Article  MathSciNet  Google Scholar 

  21. Gautam, P., V.N. Mishra, R. Ali, and S. Verma. 2021. Interpolative Chatterjea and cyclic Chatterjea contraction on quasi-partial \(b\)-metric space. AIMS Mathematics 6 (2): 1727–1742.

    Article  MathSciNet  Google Scholar 

  22. Younis, M., D. Singh, I. Altun, and V. Chauhan. 2022. Graphical structure of extended \(b\)-metric spaces: an application to the transverse oscillations of a homogeneous bar. International Journal of Nonlinear Sciences and Numerical Simulation 23 (7–8): 1239–1252.

    Article  MathSciNet  Google Scholar 

  23. Berzig, M. 2022. First results in suprametric spaces with applications. Mediterranean Journal of Mathematics 19 (5): 226.

    Article  MathSciNet  Google Scholar 

  24. Panda, S.K., K.S. Kalla, A.M. Nagy, and L. Priyanka. 2023. Numerical simulations and complex valued fractional order neural networks via \((\varepsilon -\mu )\)-uniformly contractive mappings. Chaos, Solitons and Fractals 173: 113738.

    Article  MathSciNet  Google Scholar 

  25. Panda, S.K., R.P. Agarwal, and E. Karapınar. 2023. Extended suprametric spaces and Stone-type theorem. AIMS Mathematics 8: 23183–23199.

    Article  MathSciNet  Google Scholar 

  26. Berinde, V. 1993. Generalized contractions in quasimetric spaces. In: Seminar on Fixed Point Theory, vol. 3, pp. 3–9.

  27. Van An, T., L.Q. Tuyen, and N. Van Dung. 2015. Stone-type theorem on \(b\)-metric spaces and applications. Topology and its Applications 185: 50–64.

    Article  MathSciNet  Google Scholar 

  28. Matkowski, J. 1975. Integrable solutions of functional equations. Discussiones Mathematicae 127: 1–68.

    MathSciNet  Google Scholar 

  29. Kajántó, S., and A. Lukács. 2018. A note on the paper “contraction mappings in b-metric spaces’’ by Czerwik. Acta Universitatis Sapientiae, Mathematica 10 (1): 85–89.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author thanks the referees for valuable suggestions.

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Département de Mathématiques, École Nationale Supérieure d’Ingénieurs de Tunis, Université de Tunis, 5 Avenue Taha Hussein Montfleury, 1008, Tunis, Tunisia

    Maher Berzig

Authors
  1. Maher Berzig
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maher Berzig.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by the author.

Additional information

Communicated by Simeon Reich.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Berzig, M. Nonlinear contraction in b-suprametric spaces. J Anal (2024). https://doi.org/10.1007/s41478-024-00732-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41478-024-00732-5

Keywords

Mathematics Subject Classification

Search

Navigation