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On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces

Author

Listed:
  • Manuel De la Sen

    (Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, P.O. Box 644 de Bilbao, Barrio Sarriena, 48940 Leioa (Bizkaia), Spain)

  • Mujahid Abbas

    (Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Government College University, 54000 Lahore, Pakistan)

  • Naeem Saleem

    (Department of Mathematics, National University of Computer and Emerging Sciences, Milaad Street, Lahore 54000, Pakistan
    Department of Mathematics, University of Management and Technology, C-II Johar Town, Lahore 54000, Pakistan)

Abstract

The main objective of this paper is to deal with some properties of interest in two types of fuzzy ordered proximal contractions of cyclic self-mappings T integrated in a pair ( g , T ) of mappings. In particular, g is a non-contractive fuzzy self-mapping, in the framework of non-Archimedean ordered fuzzy complete metric spaces and T is a p -cyclic proximal contraction. Two types of such contractions (so called of type I and of type II) are dealt with. In particular, the existence, uniqueness and limit properties for sequences to optimal fuzzy best proximity coincidence points are investigated for such pairs of mappings.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:2:p:22-:d:94793
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    References listed on IDEAS

    as
    1. 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.
    2. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    3. 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.
    4. Moosa Gabeleh, 2015. "Best Proximity Point Theorems via Proximal Non-self Mappings," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 565-576, February.
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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.

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