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Global optimal solutions for proximal fuzzy contractions

Author

Listed:
  • Hussain, Nawab
  • Kutbi, M.A.
  • Salimi, Peyman

Abstract

Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution x that is optimal in the sense that the error d(x,Tx) assumes the global minimum value d(A,B). In the present paper, we initiate some new classes of proximal contraction mappings and obtain best proximity point theorems for such fuzzy mappings in a non-Archimedean fuzzy metric space. As outcomes of these theorems, we conclude evident new best proximity and fixed point theorems in non-Archimedean fuzzy metric spaces with partial order. Furthermore, we provide an example to elaborate the usability of the established results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:551:y:2020:i:c:s0378437119321776
    DOI: 10.1016/j.physa.2019.123925
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    References listed on IDEAS

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    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. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, July.
    3. S. Basha, 2012. "Discrete optimization in partially ordered sets," Journal of Global Optimization, Springer, vol. 54(3), pages 511-517, November.
    4. 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.
    5. N. Hussain & S. Al-Mezel & P. Salimi, 2013. "Fixed Points for -Graphic Contractions with Application to Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, October.
    6. N. Hussain & M. A. Kutbi & P. Salimi, 2013. "Best Proximity Point Results for Modified - -Proximal Rational Contractions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, August.
    Full references (including those not matched with items on IDEAS)

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