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Best proximity point theorems: exposition of a significant non-linear programming problem

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  • S. Sadiq Basha
  • N. Shahzad
  • R. Jeyaraj

Abstract

The primary goal of this work is to address the non-linear programming problem of globally minimizing the real valued function x → d(x, Tx) where T is presumed to be a non-self mapping that is a generalized proximal contraction in the setting of a metric space. Indeed, an iterative algorithm is presented to determine a solution of the preceding non-linear programming problem that focuses on global optimization. As a sequel, one can compute optimal approximate solutions to some fixed point equations and optimal solutions to some unconstrained non-linear programming problems. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1699-1705
    DOI: 10.1007/s10898-012-9975-3
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    References listed on IDEAS

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    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. S. Sadiq Basha, 2011. "Best proximity points: global optimal approximate solutions," Journal of Global Optimization, Springer, vol. 49(1), pages 15-21, January.
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    Cited by:

    1. 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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