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Global Optimal Solutions of Noncyclic Mappings in Metric Spaces

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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.

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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 

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Correspondence to M. Gabeleh.

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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

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

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