Skip to main content
SpringerLink
Log in

The Meir–Keeler fixed point theorem in incomplete modular spaces with application

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

Abstract

In this paper, we present a new generalized modular version of the Meir–Keeler fixed point theorem endowed with an orthogonal relation. Our results improve the results of (Eshaghi Gordji et al., On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 2017). Finally, this result is applied to the existence and uniqueness of solutions to perturbed integral equations in modular function 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. Birnhaum, Z., Orlicz, W.: Uber die verallgemeinerung des begriffes der zueinander konjugierten potenzen. Studia Math. 3, 1–67 (1931)

    Article  MATH  Google Scholar 

  2. Nakano, H.: Modular Semi-ordered Spaces. Tokyo (1950)

  3. Musielak, J., Orlicz, W.: On modular spaces. Studia Math. 18, 49–65 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  4. Musielak, J.: Orlicz Spaces and Modular spaces, Lecture Notes in Math, p. 1034. Springer, Berlin (1983)

  5. Kozlowski, W.M. : Modular Function Spaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 122. Marcel Dekker, New York (1988)

  6. Khamsi, M.A., Kozlowski, W.M., Reich, S.: Fixed point theory in modular function spaces. Nonlinear Anal. TMA 14(11), 935–953 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  7. Taleb, A., Hanebaly, E.: A fixed point theorem and its application to integral equations in modular function spaces. Proc. AMS 128.2, 419–426.M (2000)

  8. Kutbi, A., Latif, A.: Fixed Points of multivalued maps in modular function spaces. Fixed Point Theory Appl. 2009, 786357-1–786357-12. doi:10.1155/2009/786357 (2009)

  9. Khamsi, M.A., Latif, A., Al–sulami, H.: KKM and KY fan theorems in modular function spaces. Fixed Point Theory Appl. 57, 2011, 57-1–57-8. doi:10.1186/1687-1812-2011-57( 2011)

  10. Khamsi, M.A., Kozlowski, W.M.: Fixed point theory in modular function spaces. Springer, New York (2015)

    Book  MATH  Google Scholar 

  11. Meir, A., Keeler, E.: A theorem on contraction mappings. J. Math. Anal. Appl. 28, 326–329 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  12. Eshaghi Gordji, M., Ramezani, M., De La Sen, M., Cho, Y.J.: On orthogonal sets and Banach fixed point theorem, Fixed Point Theory (2017) (accepted)

  13. Baghani, H., Eshaghi, M., Ramezani, M.: Orthogonal sets: the axiom of choice and proof of a fixed point theorem. J. Fixed Point Theory Appl. 18, 465–477 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  14. Baghani, H., Ramezani, M.: A fixed point theorem for a new class of set-valued mappings in \(\rm R\)-complete(not necessarily complete) metric spaces, Filomat, accepted

  15. Hadjji, A., Hanebaly, E.I.: Fixed point theorem and its application to Perturbed integral equations in modular function spaces. Electron. J. Differ. Equ. 105, 1–11 (2005)

    MathSciNet  Google Scholar 

  16. Lim, T.C.: On characterizations of Meir–Keeler contractive maps. Nonlinear Anal. 46, 113–120 (2001)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are indebted to the anonymous referees for the careful and competent reading of the present paper and for their valuable suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics Faculty of Mathematics, University of Bojnord, Bojnord, Iran

    Maryam Ramezani

  2. Department of Mathematics Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    Hamid Baghani

Authors
  1. Maryam Ramezani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamid Baghani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamid Baghani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramezani, M., Baghani, H. The Meir–Keeler fixed point theorem in incomplete modular spaces with application. J. Fixed Point Theory Appl. 19, 2369–2382 (2017). https://doi.org/10.1007/s11784-017-0440-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11784-017-0440-2

Keywords

Mathematics Subject Classification

Search

Navigation