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Best proximity results in regular cone metric spaces

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Abstract

First, we define the notion of distance between two subsets in regular cone metric spaces. Then, we establish some conditions which guarantee the existence of best proximity points for cyclic contraction map**s on regular cone metric spaces.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Di Bari, C., Vetro, P.: ϕ-pairs and common fixed points in cone metric spaces. Rend. Circ. Mat. Palermo 57, 279–285 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. 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 

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

    Article  MathSciNet  Google Scholar 

  5. Haghi, R.H., Rezapour, Sh.: Fixed points of multifunctions on regular cone metric spaces. Expo. Math. 28, 71–77 (2010)

    MathSciNet  MATH  Google Scholar 

  6. Huang, L.-G., Zhang, X.: Cone metric spaces and fixed point theorems of contractive map**s. J. Math. Anal. Appl. 332, 1468–1476 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ilić, D., Rakoc̆ević, V.: Common fixed points for maps on cone metric space. J. Math. Anal. Appl. 341, 876–882 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kirk, W.A., Sirinavasan, P.S., Veeramani, P.: Fixed points for map**s satisfying cyclical contractive conditions. Fixed Point Theory Appl. 4, 79–89 (2003)

    MATH  Google Scholar 

  9. Klim, D., Wardowski, D.: Dynamic process and fixed points of set-valued nonlinear contractions in cone metric spaces. Nonlinear Anal. 71, 5170–5175 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Petruel, G.: Cyclic representations and periodic points. Studia Univ. Babes-Bolyai. Math. 50, 107–112 (2005)

    MathSciNet  Google Scholar 

  11. Radonevic, S.: Common fixed points under contractive conditions in cone metric spaces. Comput. Math. Appl. 58, 1273–1278 (2009)

    Article  MathSciNet  Google Scholar 

  12. Rezapour, Sh., Hamlbarani Haghi, R.: Some notes on the paper “Cone metric spaces and fixed point theorems of contractive map**s”. J. Math. Anal. Appl. 345, 719–724 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rus, I.A., Petruel, A., Petruel, G.: Fixed point theorems for set-valued Y-contractions. Banach Cent. Publ. 77, 227–237 (2007)

    Article  Google Scholar 

  14. Vetro, C.: Best proximity points: convergence and existence theorems for p-cyclic map**s. Nonlinear Anal. 73, 2283–2291 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Vetro, P.: Common fixed points in cone metric spaces. Rend. Circ. Mat. Palermo 56, 464–468 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Azarbaidjan University of Tarbiat Moallem, Tabriz, Iran

    R. H. Haghi & S. Rezapour

  2. Department of Mathematics, University of Niš, Vis̆egradska 33, 18000, Niš, Serbia

    V. Rakoc̆ević

  3. Department of Mathematics, King AbdulAziz University, P.O. Box 80203, Jeddah, 21859, Saudi Arabia

    N. Shahzad

Authors
  1. R. H. Haghi
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  2. V. Rakoc̆ević
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  3. S. Rezapour
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  4. N. Shahzad
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Corresponding author

Correspondence to N. Shahzad.

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Haghi, R.H., Rakoc̆ević, V., Rezapour, S. et al. Best proximity results in regular cone metric spaces. Rend. Circ. Mat. Palermo 60, 323–327 (2011). https://doi.org/10.1007/s12215-011-0050-6

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  • DOI: https://doi.org/10.1007/s12215-011-0050-6

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