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Best proximity points: approximation and optimization

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Abstract

A best proximity point theorem explores the existence of an optimal approximate solution, known as a best proximity point, to the equations of the form Tx = x where T is a non-self mapping. The purpose of this article is to establish some best proximity point theorems for non-self non-expansive mappings, non-self Kannan- type mappings and non-self Chatterjea-type mappings, thereby producing optimal approximate solutions to some fixed point equations. Also, algorithms for determining such optimal approximate solutions are furnished in some cases.

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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 points: approximation and optimization. Optim Lett 7, 145–155 (2013). https://doi.org/10.1007/s11590-011-0404-1

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