Original Paper

Optimization Letters

, Volume 7, Issue 1, pp 145-155

Best proximity points: approximation and optimization

  • S. Sadiq BashaAffiliated withDepartment of Mathematics, Anna University Email author 
  • , N. ShahzadAffiliated withDepartment of Mathematics, King Abdul Aziz University
  • , R. JeyarajAffiliated withSt. Joseph’s College Higher Secondary School

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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.

Keywords

Optimal approximate solution Fixed point Best proximity point Contraction Cyclic contraction Non-expansive map Kannan-type mapping Chatterjea-type mapping