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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Anna University, Chennai, 600 025, India

    S. Sadiq Basha

  2. Department of Mathematics, King Abdul Aziz University, P.O.Box 80203, Jeddah, 21589, Saudi Arabia

    N. Shahzad

  3. St.Joseph’s College Higher Secondary School, Trichy, 620 002, India

    R. Jeyaraj

Authors
  1. S. Sadiq Basha
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  2. N. Shahzad
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  3. R. Jeyaraj
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Correspondence to S. Sadiq Basha.

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Sadiq Basha, S., Shahzad, N. & Jeyaraj, R. Best proximity point theorems: exposition of a significant non-linear programming problem. J Glob Optim 56, 1699–1705 (2013). https://doi.org/10.1007/s10898-012-9975-3

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  • DOI: https://doi.org/10.1007/s10898-012-9975-3

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