Skip to main content
SpringerLink
Log in

Some fixed point theorems in regular modular metric spaces and application to Caratheodory’s type anti-periodic boundary value problem

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

Abstract

In this paper, we define the concepts of \(\phi\)-contraction and point-wise \(\varPhi\)-contraction in modular metric space. Next we give some conditions that guarantee the existence and uniqueness of fixed points of self-mappings in modular metric spaces. Finally we give an application to Caratheodory’s type anti-periodic boundary value problem.

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. Abdou , A.A.N., and M.A. Khamsi. 2014. Fixed points of multivalued contraction mappings in modular metric spaces. Fixed Point Theory and Applications 249.

  2. Abdou , A.A.N., and M.A. Khamsi. 2013. Fixed point results of point-wise contractions in modular metric spaces. Fixed Point Theory and Applications 163.

  3. Aksoya, U., E. Karapınara, I. M. Erhana. 2017. Fixed point theorems in complete modular metric spaces and an application to anti-periodic boundary value problems. Filomat, 5475–5488.

  4. Al-Thagafi, M.A., and N. Shahzad. 2009. Convergence and existence results for best proximity points. Nonlinear Analytical pp. 3665–3671.

  5. Banach, S. 1922. Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fundamental Mathematics, 133–181.

  6. Chistyakov, V.V. 2010. Modular metric spaces I basic concepts. Nonlinear Analysis 72: 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  7. Chistyakov, V.V. 2011. A fixed point theorem for contractions in modular metric spaces. arXiv:1112.5561, 1–31.

  8. Chistyakov, V.V. 2013. Modular contraction and their application. Springer Proceedings in Mathematics and Statistics 32: 65–92.

    Google Scholar 

  9. Chistyakov, V.V. 2015. Metric Modular Spaces. Theory and Applications. New York: Springer.

    Book  MATH  Google Scholar 

  10. Iranmanesh, M., and A.G. Sanatee. 2018. A Common Best Proximity Point Theorem for \(\phi\)-dominated Pair. European Journal of Pure and Applied Mathematics, pp. 869–875.

  11. Jain, D., A. Padcharoen, P. Kumam, and D. Gopal. 2016. A new approach study fixed point of multivalued mapping in modular metric spaces and applications. Mathematics 4: 335–344.

    Article  MATH  Google Scholar 

  12. Khamsi, M. A., and W. M. Kozlowski. 2015. Fixed Point Theory in Modular Function Spaces, Birkhäuser.

  13. Kadelburg, Z., and S. Radenovic. 2015. Remarks on some recent M. Borcut’s results in partially ordered metric spaces. International Journal of Nonlinear Analysis and Applications 6, 96–104.

  14. Moreno, J.M., Sintunavarat, W., and Kumam, P. 2017. Banach’s contraction principle for nonlinear contraction mappings in modular metric spaces. Bulletin of the Malaysian Mathematical Sciences Society 40, 335–344

  15. C. Mongkolkeha, W. Sintunavarat and P. Kumam, Fixed point theorems for contraction mappings in modular metric spaces. Fixed Point Theory and Applications 93.

  16. Pariya, A., P. Pathak, V.H. BadshahV, and N. Gupta. 2017. Fixed point theorems for various types of compatible mappings of integral type in modular metric space. Journal of Mathematics and Informatics. 8: 7–18.

    Article  Google Scholar 

  17. Radenović, S. 2015. A note on fixed point theory for cyclic \(\phi\)-contractions. Fixed Point Theory and Applications.

  18. Rus, I.A. 2001. Generalized Contractions and Applications. Cluj University Press.

  19. Sadiq Basha, S. 2010. Extensions of Banach’s contraction principle. Numerical Functional Analysis and Optimization 31, 569–576.

  20. Sgroi, M., and C. Vetro. 2013. Multi-valued \(F\)-contractions and the solution of certain functional and integral equations. Filomat 27: 1259–1268.

    Article  MathSciNet  MATH  Google Scholar 

  21. Wardowski, D. 2012. Fixed points of new type of contractive mappings in complete metric space. Fixed Point Theory and Applications 94. https://doi.org/10.1186/1687-1812-2012-94.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quchan University of Technology, Quchan, Iran

    Ali Ganjbakhsh Sanatee

  2. Ward number - 16, Bhagatbandh, Anuppur, Madhya Pardesh, 484 224, India

    Laxmi Rathour

  3. Department of Mathematics, Faculty of Science, Indira Gandhi National Taribal University, Lalpur, Amarkantak, Anuppur, Madhya Pardesh, 484 878, India

    Vishnu Narayan Mishra

  4. Department of Mathematics, MATS School of Engineering and Information Technology, MATS University, Raipur C.G., India

    Vinita Dewangan

Authors
  1. Ali Ganjbakhsh Sanatee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laxmi Rathour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vishnu Narayan Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vinita Dewangan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vishnu Narayan Mishra.

Ethics declarations

Ethical approval

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

Additional information

Communicated by Samy Ponnusamy.

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sanatee, A.G., Rathour, L., Mishra, V.N. et al. Some fixed point theorems in regular modular metric spaces and application to Caratheodory’s type anti-periodic boundary value problem. J Anal 31, 619–632 (2023). https://doi.org/10.1007/s41478-022-00469-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41478-022-00469-z

Keywords

Mathematics Subject Classification

Search

Navigation