Skip to main content
SpringerLink
Log in

Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations

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

Abstract

In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.

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. Abbas M., Ali Khan M., Radenović S.: Common coupled fixed point theorems in cone metric spaces for w-compatible mappings. Appl. Math. Comput. 217, 195–202 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  2. Agarwal R. P., El-Gebeily M. A., O’Regan D.: Generalized contractions in partially ordered metric spaces. Appl. Anal. 87, 109–116 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. I. Altun and H. Simsek, Some fixed point theorems on ordered metric spaces and application. Fixed Point Theory Appl. 2010 (2010), Article ID 621492, 17 pages.

  4. Aydi H., Postolache M., Shatanawi W.: Coupled fixed point results for (χ, ϕ)-weakly contractive mappings in ordered G-metric spaces. Comput. Math. Appl. 63, 298–309 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  5. Banach S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund Math. 3, 133–181 (1922)

    MATH  Google Scholar 

  6. V. Berinde, Iterative Approximation of Fixed Points. 2nd ed., Lecture Notes in Math. 1912, Springer, Berlin, 2007.

  7. Berinde V.: Coupled fixed point theorems for χ-contractive mixed monotone mappings in partially ordered metric spaces. Nonlinear Anal. 75, 3218–3228 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bhaskar T. G., Lakshmikantham V.: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65, 1379–1393 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Binayak S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings. Nonlinear Anal. 73 (2010), 2524–2531.

  10. L. ćirić, N. Cakić, M. Rajović and J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces. Fixed Point Theory Appl. 2008 (2008), Article ID 131294, 11 pages.

  11. W.-S. Du, Coupled fixed point theorems for nonlinear contractions satisfied Mizoguchi-Takahashi’s condition in Quasiordered metric spaces. Fixed Point Theory Appl. 2010 (2010), Article ID 876372, 9 pages.

  12. Harjani J., Sadarangani K.: Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations. Nonlinear Anal. 72, 1188–1197 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  13. Karapinar E.: Couple fixed point theorems for nonlinear contractions in cone metric spaces. Comput. Math. Appl. 59, 3656–3668 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lakshmikantham V., Ćirić L: Coupled fixed point theorems for nonlinear contractions in partially ordered metric space. Nonlinear Anal. 70, 4341–4349 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  15. Luong N. V., Thuan N. X.: Coupled fixed points in partially ordered metric spaces and application. Nonlinear Anal. 74, 983–992 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  16. Nieto J. J., López R. R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22, 223–239 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. J. J. Nieto and R. R. López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sin. (Engl. Ser.) 23 (2007), 2205–2212.

    Google Scholar 

  18. O’Regan D., PetruA.el A.: Fixed point theorems for generalized contractions in ordered metric spaces. J. Math. Anal. Appl. 341, 1241–1252 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Ran A. C. M., Reurings M. C. B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Amer. Math. Soc. 132, 1435–1443 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  20. Rus I. A., Petruşel A., Petruşel G.: Fixed Point Theory. Cluj University Press, Cluj-Napoca (2008)

    MATH  Google Scholar 

  21. Samet B., Vetro C.: Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. Nonlinear Anal. 74, 4260–4268 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  22. Samet B., Vetro C., Vetro P.: Fixed point theorems for α-ψ-contractive type mappings. Nonlinear Anal. 75, 2154–2165 (2012)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, King Saud University, Riyath, Saudi Arabia

    Mohamed Jleli & Bessem Samet

  2. Faculty of Economics, University of Belgrade, Kamenička 6, 11000, Beograd, Serbia

    Vesna Čojbašić Rajić

  3. Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi, 34, 90123, Palermo, Italy

    Calogero Vetro

Authors
  1. Mohamed Jleli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vesna Čojbašić Rajić
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bessem Samet
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Calogero Vetro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bessem Samet.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jleli, M., Čojbašić Rajić, V., Samet, B. et al. Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations. J. Fixed Point Theory Appl. 12, 175–192 (2012). https://doi.org/10.1007/s11784-012-0081-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11784-012-0081-4

Mathematics Subject Classification

Keywords

Search

Navigation