Skip to main content
SpringerLink
Log in

An optimization problem under partial order constraints on a metric space

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

Abstract

We establish an existence result for a minimization problem subject to two inequality constraints with respect to two partial orders defined on a complete metric space.

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. Abkar, A., Gabeleh, M.: Best proximity points for cyclic mappings in ordered metric spaces. J. Optim. Theory Appl. 150, 188–193 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abkar, A., Gabeleh, M.: Generalized cyclic contractions in partially ordered metric spaces. Optim. Lett. 6, 1819–1830 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Al-Thagafi, M.A., Shahzad, N.: Convergence and existence results for best proximity points. Nonlinear Anal. 70, 3665–3671 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ansari, A.H., Kumam, P., Samet, B.: A fixed point problem with constraint inequalities via an implicit contraction. J. Fixed Point Theory Appl. 19(2), 1145–1163 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  5. Anthony Eldred, A., Veeramani, P.: Existence and convergence of best proximity points. J. Math. Anal. Appl. 323, 1001–1006 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Berinde, V.: Generalized Contractions and Applications (in Romanian), vol. 22. Editura Cub Press, Baia Mare (1997)

    MATH  Google Scholar 

  7. Di Bari, C., Suzuki, T., Vetro, C.: Best proximity points for cyclic Meir-Keeler contractions. Nonlinear Anal. 69, 3790–3794 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jleli, M., Samet, B.: A fixed point problem under two constraint inequalities. Fixed Point Theory Appl. 18, 1–14 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kirk, W.A., Reich, S., Veeramani, P.: Proximinal retracts and best proximity pair theorems. Numer. Funct. Anal. Optim. 24, 851–862 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Basha, SSadiq: Best proximity point theorems generalizing the contraction principle. Nonlinear Anal. 74, 5844–5850 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sadiq Basha, S., Veeramani, P.: Best proximity pair theorems for multifunctions with open fibres. J. Approx. Theory. 103, 119–129 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Samet, B., Vetro, C., Vetro, F.: An approximate fixed point result for multivalued mappings under two constraint inequalities. J. Fixed Point Theory Appl. 19(3), 2095–2107 (2017)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The third author extends his appreciation to Distinguished Scientist Fellowship Program (DSFP) at King Saud University (Saudi Arabia).

Author information

Authors and Affiliations

  1. Islamic Azad University, Karaj, Iran

    Arslan Hojat Ansari

  2. Bharathidasan University, Tiruchirappalli, Tamil Nadu, India

    Geno Kadwin Jacob

  3. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Bessem Samet

Authors
  1. Arslan Hojat Ansari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Geno Kadwin Jacob
    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

Corresponding author

Correspondence to Bessem Samet.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ansari, A.H., Jacob, G.K. & Samet, B. An optimization problem under partial order constraints on a metric space. J. Fixed Point Theory Appl. 20, 26 (2018). https://doi.org/10.1007/s11784-018-0514-9

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s11784-018-0514-9

Mathematics Subject Classification

Keywords

Search

Navigation