Skip to main content

Global Optimal Solutions of Noncyclic Mappings in Metric Spaces

Journal of Optimization Theory and Applications volume 153, pages 298–305 (2012)Cite this article

Abstract

We study some minimization problems for noncyclic mappings in metric spaces. We then apply the solution to obtain some results in the theory of analytic functions.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

39,95 €

Price includes VAT (Finland)

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Abkar, A., Gabeleh, M.: Results on the existence and convergence of best proximity points. Fixed Point Theory Appl. 2010, 386037 (2010), 10 pp.

    Article  MathSciNet  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. Suzuki, T., Kikkawa, M., Vetro, C.: The existence of best proximity points in metric spaces with the property UC. Nonlinear Anal. 71, 2918–2926 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Derafshpour, M., Rezapour, Sh., Shahzad, N.: Best proximity points of cyclic φ-contractions in ordered metric spaces. Topol. Methods Nonlinear Anal. 37, 193–202 (2011)

    MathSciNet  MATH  Google Scholar 

  6. 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 

  7. Wlodarczyk, K., Plebaniak, R., Banach, A.: Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces. Nonlinear Anal. 70, 3332–3341 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wlodarczyk, K., Plebaniak, R., Banach, A.: Erratum to: “Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces”. Nonlinear Anal. (2008). doi:10.1016/j.na.2008.04.037. Nonlinear Anal. 71(7–8), 3585–3586 (2009)

    Google Scholar 

  9. 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 

  10. Vetro, C.: Best proximity points: convergence and existence theorems for p-cyclic mappings. Nonlinear Anal. 73(7), 2283–2291 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Eldred, A., Kirk, W.A., Veeramani, P.: Proximal normal structure and relatively nonexpansive mappings. Stud. Math. 171(3), 283–293 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sankar Raj, V.: A best proximity point theorem for weakly contractive non-self-mappings. Nonlinear Anal. 74, 4804–4808 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Khamsi, M.A., Kirk, W.A.: An Introduction to Metric Spaces and Fixed Point Theory. Wiley, New York (2001)

    Book  Google Scholar 

  14. Sadiq Basha, S.: Best proximity points: global optimal approximate solutions. J. Glob. Optim. (2011). doi:10.1007/s10898-009-9521-0

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Imam Khomeini International University, Qazvin, 34149, Iran

    A. Abkar & M. Gabeleh

Authors
  1. A. Abkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Gabeleh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Gabeleh.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Abkar, A., Gabeleh, M. Global Optimal Solutions of Noncyclic Mappings in Metric Spaces. J Optim Theory Appl 153, 298–305 (2012). https://doi.org/10.1007/s10957-011-9966-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-011-9966-4

Keywords

  • Noncyclic mapping
  • Contraction mapping
  • Nonexpansive mapping
  • Fixed point