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Best proximity point results in non-Archimedean fuzzy metric spaces

Author

Listed:
  • Calogero Vetro

    (Università degli Studi di Palermo)

  • Peyman Salimi

    (Islamic Azad University)

Abstract

We consider the problem of finding a best proximity point which achieves the minimum distance between two nonempty sets in a non-Archimedean fuzzy metric space. First we prove the existence and uniqueness of the best proximity point by using different contractive conditions, then we present some examples to support our best proximity point theorems.

Suggested Citation

  • Calogero Vetro & Peyman Salimi, 2013. "Best proximity point results in non-Archimedean fuzzy metric spaces," Fuzzy Information and Engineering, Springer, vol. 5(4), pages 417-429, December.
    • Handle: RePEc:spr:fuzinf:v:5:y:2013:i:4:d:10.1007_s12543-013-0155-z
    DOI: 10.1007/s12543-013-0155-z
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    References listed on IDEAS

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    1. S. Basha, 2012. "Discrete optimization in partially ordered sets," Journal of Global Optimization, Springer, vol. 54(3), pages 511-517, November.
    2. S. Sadiq Basha, 2012. "Common best proximity points: global minimization of multi-objective functions," Journal of Global Optimization, Springer, vol. 54(2), pages 367-373, October.
    3. S. Sadiq Basha & N. Shahzad & R. Jeyaraj, 2013. "Best proximity point theorems: exposition of a significant non-linear programming problem," Journal of Global Optimization, Springer, vol. 56(4), pages 1699-1705, August.
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    Citations

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    Cited by:

    1. Mi Zhou & Naeem Saleem & Antonio Francisco Roldán López de Hierro & Xiaolan Liu, 2022. "Best Proximity Point Theorems without Fuzzy P -Property for Several ( ψ − ϕ )-Weak Contractions in Non-Archimedean Fuzzy Metric Spaces," Mathematics, MDPI, vol. 10(21), pages 1-27, October.
    2. Naeem Saleem & Mujahid Abbas & Manuel De la Sen, 2019. "Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces," Mathematics, MDPI, vol. 7(4), pages 1-13, April.
    3. Manuel De la Sen & Mujahid Abbas & Naeem Saleem, 2017. "On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces," Mathematics, MDPI, vol. 5(2), pages 1-20, April.
    4. Hussain, Nawab & Kutbi, M.A. & Salimi, Peyman, 2020. "Global optimal solutions for proximal fuzzy contractions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).

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