Optimization Letters

, Volume 7, Issue 1, pp 145–155

Best proximity points: approximation and optimization


    • Department of MathematicsAnna University
  • N. Shahzad
    • Department of MathematicsKing Abdul Aziz University
  • R. Jeyaraj
    • St. Joseph’s College Higher Secondary School
Original Paper

DOI: 10.1007/s11590-011-0404-1

Cite this article as:
Sadiq Basha, S., Shahzad, N. & Jeyaraj, R. Optim Lett (2013) 7: 145. doi:10.1007/s11590-011-0404-1


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.


Optimal approximate solutionFixed pointBest proximity pointContractionCyclic contractionNon-expansive mapKannan-type mappingChatterjea-type mapping

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© Springer-Verlag 2011