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Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces

Author

Listed:
  • Naeem Saleem

    (Department of Mathematics, University of Management and Technology, C-II Johar Town, Lahore 54000, Pakistan)

  • Mujahid Abbas

    (Department of Mathematics, Government College University, Lahore 54000, Pakistan
    Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa)

  • 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)

Abstract

The purpose of this paper is to introduce α f -proximal H -contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable results in the literature. We also present some examples to support the results obtained herein.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:327-:d:219766
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    References listed on IDEAS

    as
    1. N. Shahzad & S. Sadiq Basha & R. Jeyaraj, 2011. "Common Best Proximity Points: Global Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 69-78, January.
    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.
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