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Best proximity point theorems: resolution of an important non-linear programming problem

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Abstract

The purpose of this article is to resolve the non-linear programming problem of globally minimizing the real valued function \({x \longrightarrow d(x, Sx)}\) where S is a non-self-mapping in the setting of a metric space with the distance function ‘d’. An iterative algorithm is also furnished to find a solution of such global optimization problems. As a consequence, one can determine an optimal approximate solution to some equations of the form Sx = x.

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Authors and Affiliations

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

    S. Sadiq Basha

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Basha, S.S. Best proximity point theorems: resolution of an important non-linear programming problem. Optim Lett 7, 1167–1177 (2013). https://doi.org/10.1007/s11590-012-0493-5

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